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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.util;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.PrintStream;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    /**<a name="line.21"></a>
<FONT color="green">022</FONT>     * Faster, more accurate, portable alternative to {@link Math} and<a name="line.22"></a>
<FONT color="green">023</FONT>     * {@link StrictMath} for large scale computation.<a name="line.23"></a>
<FONT color="green">024</FONT>     * &lt;p&gt;<a name="line.24"></a>
<FONT color="green">025</FONT>     * FastMath is a drop-in replacement for both Math and StrictMath. This<a name="line.25"></a>
<FONT color="green">026</FONT>     * means that for any method in Math (say {@code Math.sin(x)} or<a name="line.26"></a>
<FONT color="green">027</FONT>     * {@code Math.cbrt(y)}), user can directly change the class and use the<a name="line.27"></a>
<FONT color="green">028</FONT>     * methods as is (using {@code FastMath.sin(x)} or {@code FastMath.cbrt(y)}<a name="line.28"></a>
<FONT color="green">029</FONT>     * in the previous example).<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * FastMath speed is achieved by relying heavily on optimizing compilers<a name="line.32"></a>
<FONT color="green">033</FONT>     * to native code present in many JVMs today and use of large tables.<a name="line.33"></a>
<FONT color="green">034</FONT>     * The larger tables are lazily initialised on first use, so that the setup<a name="line.34"></a>
<FONT color="green">035</FONT>     * time does not penalise methods that don't need them.<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;/p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * Note that FastMath is<a name="line.38"></a>
<FONT color="green">039</FONT>     * extensively used inside Apache Commons Math, so by calling some algorithms,<a name="line.39"></a>
<FONT color="green">040</FONT>     * the overhead when the the tables need to be intialised will occur<a name="line.40"></a>
<FONT color="green">041</FONT>     * regardless of the end-user calling FastMath methods directly or not.<a name="line.41"></a>
<FONT color="green">042</FONT>     * Performance figures for a specific JVM and hardware can be evaluated by<a name="line.42"></a>
<FONT color="green">043</FONT>     * running the FastMathTestPerformance tests in the test directory of the source<a name="line.43"></a>
<FONT color="green">044</FONT>     * distribution.<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;/p&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;p&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * FastMath accuracy should be mostly independent of the JVM as it relies only<a name="line.47"></a>
<FONT color="green">048</FONT>     * on IEEE-754 basic operations and on embedded tables. Almost all operations<a name="line.48"></a>
<FONT color="green">049</FONT>     * are accurate to about 0.5 ulp throughout the domain range. This statement,<a name="line.49"></a>
<FONT color="green">050</FONT>     * of course is only a rough global observed behavior, it is &lt;em&gt;not&lt;/em&gt; a<a name="line.50"></a>
<FONT color="green">051</FONT>     * guarantee for &lt;em&gt;every&lt;/em&gt; double numbers input (see William Kahan's &lt;a<a name="line.51"></a>
<FONT color="green">052</FONT>     * href="http://en.wikipedia.org/wiki/Rounding#The_table-maker.27s_dilemma"&gt;Table<a name="line.52"></a>
<FONT color="green">053</FONT>     * Maker's Dilemma&lt;/a&gt;).<a name="line.53"></a>
<FONT color="green">054</FONT>     * &lt;/p&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     * &lt;p&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     * FastMath additionally implements the following methods not found in Math/StrictMath:<a name="line.56"></a>
<FONT color="green">057</FONT>     * &lt;ul&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * &lt;li&gt;{@link #asinh(double)}&lt;/li&gt;<a name="line.58"></a>
<FONT color="green">059</FONT>     * &lt;li&gt;{@link #acosh(double)}&lt;/li&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     * &lt;li&gt;{@link #atanh(double)}&lt;/li&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     * &lt;/ul&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>     * The following methods are found in Math/StrictMath since 1.6 only, they are provided<a name="line.62"></a>
<FONT color="green">063</FONT>     * by FastMath even in 1.5 Java virtual machines<a name="line.63"></a>
<FONT color="green">064</FONT>     * &lt;ul&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>     * &lt;li&gt;{@link #copySign(double, double)}&lt;/li&gt;<a name="line.65"></a>
<FONT color="green">066</FONT>     * &lt;li&gt;{@link #getExponent(double)}&lt;/li&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;li&gt;{@link #nextAfter(double,double)}&lt;/li&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     * &lt;li&gt;{@link #nextUp(double)}&lt;/li&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>     * &lt;li&gt;{@link #scalb(double, int)}&lt;/li&gt;<a name="line.69"></a>
<FONT color="green">070</FONT>     * &lt;li&gt;{@link #copySign(float, float)}&lt;/li&gt;<a name="line.70"></a>
<FONT color="green">071</FONT>     * &lt;li&gt;{@link #getExponent(float)}&lt;/li&gt;<a name="line.71"></a>
<FONT color="green">072</FONT>     * &lt;li&gt;{@link #nextAfter(float,double)}&lt;/li&gt;<a name="line.72"></a>
<FONT color="green">073</FONT>     * &lt;li&gt;{@link #nextUp(float)}&lt;/li&gt;<a name="line.73"></a>
<FONT color="green">074</FONT>     * &lt;li&gt;{@link #scalb(float, int)}&lt;/li&gt;<a name="line.74"></a>
<FONT color="green">075</FONT>     * &lt;/ul&gt;<a name="line.75"></a>
<FONT color="green">076</FONT>     * &lt;/p&gt;<a name="line.76"></a>
<FONT color="green">077</FONT>     * @version $Id: FastMath.java 1422313 2012-12-15 18:53:41Z psteitz $<a name="line.77"></a>
<FONT color="green">078</FONT>     * @since 2.2<a name="line.78"></a>
<FONT color="green">079</FONT>     */<a name="line.79"></a>
<FONT color="green">080</FONT>    public class FastMath {<a name="line.80"></a>
<FONT color="green">081</FONT>        /** Archimede's constant PI, ratio of circle circumference to diameter. */<a name="line.81"></a>
<FONT color="green">082</FONT>        public static final double PI = 105414357.0 / 33554432.0 + 1.984187159361080883e-9;<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>        /** Napier's constant e, base of the natural logarithm. */<a name="line.84"></a>
<FONT color="green">085</FONT>        public static final double E = 2850325.0 / 1048576.0 + 8.254840070411028747e-8;<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /** Index of exp(0) in the array of integer exponentials. */<a name="line.87"></a>
<FONT color="green">088</FONT>        static final int EXP_INT_TABLE_MAX_INDEX = 750;<a name="line.88"></a>
<FONT color="green">089</FONT>        /** Length of the array of integer exponentials. */<a name="line.89"></a>
<FONT color="green">090</FONT>        static final int EXP_INT_TABLE_LEN = EXP_INT_TABLE_MAX_INDEX * 2;<a name="line.90"></a>
<FONT color="green">091</FONT>        /** Logarithm table length. */<a name="line.91"></a>
<FONT color="green">092</FONT>        static final int LN_MANT_LEN = 1024;<a name="line.92"></a>
<FONT color="green">093</FONT>        /** Exponential fractions table length. */<a name="line.93"></a>
<FONT color="green">094</FONT>        static final int EXP_FRAC_TABLE_LEN = 1025; // 0, 1/1024, ... 1024/1024<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        /** StrictMath.log(Double.MAX_VALUE): {@value} */<a name="line.96"></a>
<FONT color="green">097</FONT>        private static final double LOG_MAX_VALUE = StrictMath.log(Double.MAX_VALUE);<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /** Indicator for tables initialization.<a name="line.99"></a>
<FONT color="green">100</FONT>         * &lt;p&gt;<a name="line.100"></a>
<FONT color="green">101</FONT>         * This compile-time constant should be set to true only if one explicitly<a name="line.101"></a>
<FONT color="green">102</FONT>         * wants to compute the tables at class loading time instead of using the<a name="line.102"></a>
<FONT color="green">103</FONT>         * already computed ones provided as literal arrays below.<a name="line.103"></a>
<FONT color="green">104</FONT>         * &lt;/p&gt;<a name="line.104"></a>
<FONT color="green">105</FONT>         */<a name="line.105"></a>
<FONT color="green">106</FONT>        private static final boolean RECOMPUTE_TABLES_AT_RUNTIME = false;<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>        /** log(2) (high bits). */<a name="line.108"></a>
<FONT color="green">109</FONT>        private static final double LN_2_A = 0.693147063255310059;<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>        /** log(2) (low bits). */<a name="line.111"></a>
<FONT color="green">112</FONT>        private static final double LN_2_B = 1.17304635250823482e-7;<a name="line.112"></a>
<FONT color="green">113</FONT>    <a name="line.113"></a>
<FONT color="green">114</FONT>        /** Coefficients for log, when input 0.99 &lt; x &lt; 1.01. */<a name="line.114"></a>
<FONT color="green">115</FONT>        private static final double LN_QUICK_COEF[][] = {<a name="line.115"></a>
<FONT color="green">116</FONT>            {1.0, 5.669184079525E-24},<a name="line.116"></a>
<FONT color="green">117</FONT>            {-0.25, -0.25},<a name="line.117"></a>
<FONT color="green">118</FONT>            {0.3333333134651184, 1.986821492305628E-8},<a name="line.118"></a>
<FONT color="green">119</FONT>            {-0.25, -6.663542893624021E-14},<a name="line.119"></a>
<FONT color="green">120</FONT>            {0.19999998807907104, 1.1921056801463227E-8},<a name="line.120"></a>
<FONT color="green">121</FONT>            {-0.1666666567325592, -7.800414592973399E-9},<a name="line.121"></a>
<FONT color="green">122</FONT>            {0.1428571343421936, 5.650007086920087E-9},<a name="line.122"></a>
<FONT color="green">123</FONT>            {-0.12502530217170715, -7.44321345601866E-11},<a name="line.123"></a>
<FONT color="green">124</FONT>            {0.11113807559013367, 9.219544613762692E-9},<a name="line.124"></a>
<FONT color="green">125</FONT>        };<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>        /** Coefficients for log in the range of 1.0 &lt; x &lt; 1.0 + 2^-10. */<a name="line.127"></a>
<FONT color="green">128</FONT>        private static final double LN_HI_PREC_COEF[][] = {<a name="line.128"></a>
<FONT color="green">129</FONT>            {1.0, -6.032174644509064E-23},<a name="line.129"></a>
<FONT color="green">130</FONT>            {-0.25, -0.25},<a name="line.130"></a>
<FONT color="green">131</FONT>            {0.3333333134651184, 1.9868161777724352E-8},<a name="line.131"></a>
<FONT color="green">132</FONT>            {-0.2499999701976776, -2.957007209750105E-8},<a name="line.132"></a>
<FONT color="green">133</FONT>            {0.19999954104423523, 1.5830993332061267E-10},<a name="line.133"></a>
<FONT color="green">134</FONT>            {-0.16624879837036133, -2.6033824355191673E-8}<a name="line.134"></a>
<FONT color="green">135</FONT>        };<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>        /** Sine, Cosine, Tangent tables are for 0, 1/8, 2/8, ... 13/8 = PI/2 approx. */<a name="line.137"></a>
<FONT color="green">138</FONT>        private static final int SINE_TABLE_LEN = 14;<a name="line.138"></a>
<FONT color="green">139</FONT>    <a name="line.139"></a>
<FONT color="green">140</FONT>        /** Sine table (high bits). */<a name="line.140"></a>
<FONT color="green">141</FONT>        private static final double SINE_TABLE_A[] =<a name="line.141"></a>
<FONT color="green">142</FONT>            {<a name="line.142"></a>
<FONT color="green">143</FONT>            +0.0d,<a name="line.143"></a>
<FONT color="green">144</FONT>            +0.1246747374534607d,<a name="line.144"></a>
<FONT color="green">145</FONT>            +0.24740394949913025d,<a name="line.145"></a>
<FONT color="green">146</FONT>            +0.366272509098053d,<a name="line.146"></a>
<FONT color="green">147</FONT>            +0.4794255495071411d,<a name="line.147"></a>
<FONT color="green">148</FONT>            +0.5850973129272461d,<a name="line.148"></a>
<FONT color="green">149</FONT>            +0.6816387176513672d,<a name="line.149"></a>
<FONT color="green">150</FONT>            +0.7675435543060303d,<a name="line.150"></a>
<FONT color="green">151</FONT>            +0.8414709568023682d,<a name="line.151"></a>
<FONT color="green">152</FONT>            +0.902267575263977d,<a name="line.152"></a>
<FONT color="green">153</FONT>            +0.9489846229553223d,<a name="line.153"></a>
<FONT color="green">154</FONT>            +0.9808930158615112d,<a name="line.154"></a>
<FONT color="green">155</FONT>            +0.9974949359893799d,<a name="line.155"></a>
<FONT color="green">156</FONT>            +0.9985313415527344d,<a name="line.156"></a>
<FONT color="green">157</FONT>        };<a name="line.157"></a>
<FONT color="green">158</FONT>    <a name="line.158"></a>
<FONT color="green">159</FONT>        /** Sine table (low bits). */<a name="line.159"></a>
<FONT color="green">160</FONT>        private static final double SINE_TABLE_B[] =<a name="line.160"></a>
<FONT color="green">161</FONT>            {<a name="line.161"></a>
<FONT color="green">162</FONT>            +0.0d,<a name="line.162"></a>
<FONT color="green">163</FONT>            -4.068233003401932E-9d,<a name="line.163"></a>
<FONT color="green">164</FONT>            +9.755392680573412E-9d,<a name="line.164"></a>
<FONT color="green">165</FONT>            +1.9987994582857286E-8d,<a name="line.165"></a>
<FONT color="green">166</FONT>            -1.0902938113007961E-8d,<a name="line.166"></a>
<FONT color="green">167</FONT>            -3.9986783938944604E-8d,<a name="line.167"></a>
<FONT color="green">168</FONT>            +4.23719669792332E-8d,<a name="line.168"></a>
<FONT color="green">169</FONT>            -5.207000323380292E-8d,<a name="line.169"></a>
<FONT color="green">170</FONT>            +2.800552834259E-8d,<a name="line.170"></a>
<FONT color="green">171</FONT>            +1.883511811213715E-8d,<a name="line.171"></a>
<FONT color="green">172</FONT>            -3.5997360512765566E-9d,<a name="line.172"></a>
<FONT color="green">173</FONT>            +4.116164446561962E-8d,<a name="line.173"></a>
<FONT color="green">174</FONT>            +5.0614674548127384E-8d,<a name="line.174"></a>
<FONT color="green">175</FONT>            -1.0129027912496858E-9d,<a name="line.175"></a>
<FONT color="green">176</FONT>        };<a name="line.176"></a>
<FONT color="green">177</FONT>    <a name="line.177"></a>
<FONT color="green">178</FONT>        /** Cosine table (high bits). */<a name="line.178"></a>
<FONT color="green">179</FONT>        private static final double COSINE_TABLE_A[] =<a name="line.179"></a>
<FONT color="green">180</FONT>            {<a name="line.180"></a>
<FONT color="green">181</FONT>            +1.0d,<a name="line.181"></a>
<FONT color="green">182</FONT>            +0.9921976327896118d,<a name="line.182"></a>
<FONT color="green">183</FONT>            +0.9689123630523682d,<a name="line.183"></a>
<FONT color="green">184</FONT>            +0.9305076599121094d,<a name="line.184"></a>
<FONT color="green">185</FONT>            +0.8775825500488281d,<a name="line.185"></a>
<FONT color="green">186</FONT>            +0.8109631538391113d,<a name="line.186"></a>
<FONT color="green">187</FONT>            +0.7316888570785522d,<a name="line.187"></a>
<FONT color="green">188</FONT>            +0.6409968137741089d,<a name="line.188"></a>
<FONT color="green">189</FONT>            +0.5403022766113281d,<a name="line.189"></a>
<FONT color="green">190</FONT>            +0.4311765432357788d,<a name="line.190"></a>
<FONT color="green">191</FONT>            +0.3153223395347595d,<a name="line.191"></a>
<FONT color="green">192</FONT>            +0.19454771280288696d,<a name="line.192"></a>
<FONT color="green">193</FONT>            +0.07073719799518585d,<a name="line.193"></a>
<FONT color="green">194</FONT>            -0.05417713522911072d,<a name="line.194"></a>
<FONT color="green">195</FONT>        };<a name="line.195"></a>
<FONT color="green">196</FONT>    <a name="line.196"></a>
<FONT color="green">197</FONT>        /** Cosine table (low bits). */<a name="line.197"></a>
<FONT color="green">198</FONT>        private static final double COSINE_TABLE_B[] =<a name="line.198"></a>
<FONT color="green">199</FONT>            {<a name="line.199"></a>
<FONT color="green">200</FONT>            +0.0d,<a name="line.200"></a>
<FONT color="green">201</FONT>            +3.4439717236742845E-8d,<a name="line.201"></a>
<FONT color="green">202</FONT>            +5.865827662008209E-8d,<a name="line.202"></a>
<FONT color="green">203</FONT>            -3.7999795083850525E-8d,<a name="line.203"></a>
<FONT color="green">204</FONT>            +1.184154459111628E-8d,<a name="line.204"></a>
<FONT color="green">205</FONT>            -3.43338934259355E-8d,<a name="line.205"></a>
<FONT color="green">206</FONT>            +1.1795268640216787E-8d,<a name="line.206"></a>
<FONT color="green">207</FONT>            +4.438921624363781E-8d,<a name="line.207"></a>
<FONT color="green">208</FONT>            +2.925681159240093E-8d,<a name="line.208"></a>
<FONT color="green">209</FONT>            -2.6437112632041807E-8d,<a name="line.209"></a>
<FONT color="green">210</FONT>            +2.2860509143963117E-8d,<a name="line.210"></a>
<FONT color="green">211</FONT>            -4.813899778443457E-9d,<a name="line.211"></a>
<FONT color="green">212</FONT>            +3.6725170580355583E-9d,<a name="line.212"></a>
<FONT color="green">213</FONT>            +2.0217439756338078E-10d,<a name="line.213"></a>
<FONT color="green">214</FONT>        };<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>    <a name="line.216"></a>
<FONT color="green">217</FONT>        /** Tangent table, used by atan() (high bits). */<a name="line.217"></a>
<FONT color="green">218</FONT>        private static final double TANGENT_TABLE_A[] =<a name="line.218"></a>
<FONT color="green">219</FONT>            {<a name="line.219"></a>
<FONT color="green">220</FONT>            +0.0d,<a name="line.220"></a>
<FONT color="green">221</FONT>            +0.1256551444530487d,<a name="line.221"></a>
<FONT color="green">222</FONT>            +0.25534194707870483d,<a name="line.222"></a>
<FONT color="green">223</FONT>            +0.3936265707015991d,<a name="line.223"></a>
<FONT color="green">224</FONT>            +0.5463024377822876d,<a name="line.224"></a>
<FONT color="green">225</FONT>            +0.7214844226837158d,<a name="line.225"></a>
<FONT color="green">226</FONT>            +0.9315965175628662d,<a name="line.226"></a>
<FONT color="green">227</FONT>            +1.1974215507507324d,<a name="line.227"></a>
<FONT color="green">228</FONT>            +1.5574076175689697d,<a name="line.228"></a>
<FONT color="green">229</FONT>            +2.092571258544922d,<a name="line.229"></a>
<FONT color="green">230</FONT>            +3.0095696449279785d,<a name="line.230"></a>
<FONT color="green">231</FONT>            +5.041914939880371d,<a name="line.231"></a>
<FONT color="green">232</FONT>            +14.101419448852539d,<a name="line.232"></a>
<FONT color="green">233</FONT>            -18.430862426757812d,<a name="line.233"></a>
<FONT color="green">234</FONT>        };<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>        /** Tangent table, used by atan() (low bits). */<a name="line.236"></a>
<FONT color="green">237</FONT>        private static final double TANGENT_TABLE_B[] =<a name="line.237"></a>
<FONT color="green">238</FONT>            {<a name="line.238"></a>
<FONT color="green">239</FONT>            +0.0d,<a name="line.239"></a>
<FONT color="green">240</FONT>            -7.877917738262007E-9d,<a name="line.240"></a>
<FONT color="green">241</FONT>            -2.5857668567479893E-8d,<a name="line.241"></a>
<FONT color="green">242</FONT>            +5.2240336371356666E-9d,<a name="line.242"></a>
<FONT color="green">243</FONT>            +5.206150291559893E-8d,<a name="line.243"></a>
<FONT color="green">244</FONT>            +1.8307188599677033E-8d,<a name="line.244"></a>
<FONT color="green">245</FONT>            -5.7618793749770706E-8d,<a name="line.245"></a>
<FONT color="green">246</FONT>            +7.848361555046424E-8d,<a name="line.246"></a>
<FONT color="green">247</FONT>            +1.0708593250394448E-7d,<a name="line.247"></a>
<FONT color="green">248</FONT>            +1.7827257129423813E-8d,<a name="line.248"></a>
<FONT color="green">249</FONT>            +2.893485277253286E-8d,<a name="line.249"></a>
<FONT color="green">250</FONT>            +3.1660099222737955E-7d,<a name="line.250"></a>
<FONT color="green">251</FONT>            +4.983191803254889E-7d,<a name="line.251"></a>
<FONT color="green">252</FONT>            -3.356118100840571E-7d,<a name="line.252"></a>
<FONT color="green">253</FONT>        };<a name="line.253"></a>
<FONT color="green">254</FONT>    <a name="line.254"></a>
<FONT color="green">255</FONT>        /** Bits of 1/(2*pi), need for reducePayneHanek(). */<a name="line.255"></a>
<FONT color="green">256</FONT>        private static final long RECIP_2PI[] = new long[] {<a name="line.256"></a>
<FONT color="green">257</FONT>            (0x28be60dbL &lt;&lt; 32) | 0x9391054aL,<a name="line.257"></a>
<FONT color="green">258</FONT>            (0x7f09d5f4L &lt;&lt; 32) | 0x7d4d3770L,<a name="line.258"></a>
<FONT color="green">259</FONT>            (0x36d8a566L &lt;&lt; 32) | 0x4f10e410L,<a name="line.259"></a>
<FONT color="green">260</FONT>            (0x7f9458eaL &lt;&lt; 32) | 0xf7aef158L,<a name="line.260"></a>
<FONT color="green">261</FONT>            (0x6dc91b8eL &lt;&lt; 32) | 0x909374b8L,<a name="line.261"></a>
<FONT color="green">262</FONT>            (0x01924bbaL &lt;&lt; 32) | 0x82746487L,<a name="line.262"></a>
<FONT color="green">263</FONT>            (0x3f877ac7L &lt;&lt; 32) | 0x2c4a69cfL,<a name="line.263"></a>
<FONT color="green">264</FONT>            (0xba208d7dL &lt;&lt; 32) | 0x4baed121L,<a name="line.264"></a>
<FONT color="green">265</FONT>            (0x3a671c09L &lt;&lt; 32) | 0xad17df90L,<a name="line.265"></a>
<FONT color="green">266</FONT>            (0x4e64758eL &lt;&lt; 32) | 0x60d4ce7dL,<a name="line.266"></a>
<FONT color="green">267</FONT>            (0x272117e2L &lt;&lt; 32) | 0xef7e4a0eL,<a name="line.267"></a>
<FONT color="green">268</FONT>            (0xc7fe25ffL &lt;&lt; 32) | 0xf7816603L,<a name="line.268"></a>
<FONT color="green">269</FONT>            (0xfbcbc462L &lt;&lt; 32) | 0xd6829b47L,<a name="line.269"></a>
<FONT color="green">270</FONT>            (0xdb4d9fb3L &lt;&lt; 32) | 0xc9f2c26dL,<a name="line.270"></a>
<FONT color="green">271</FONT>            (0xd3d18fd9L &lt;&lt; 32) | 0xa797fa8bL,<a name="line.271"></a>
<FONT color="green">272</FONT>            (0x5d49eeb1L &lt;&lt; 32) | 0xfaf97c5eL,<a name="line.272"></a>
<FONT color="green">273</FONT>            (0xcf41ce7dL &lt;&lt; 32) | 0xe294a4baL,<a name="line.273"></a>
<FONT color="green">274</FONT>             0x9afed7ecL &lt;&lt; 32  };<a name="line.274"></a>
<FONT color="green">275</FONT>    <a name="line.275"></a>
<FONT color="green">276</FONT>        /** Bits of pi/4, need for reducePayneHanek(). */<a name="line.276"></a>
<FONT color="green">277</FONT>        private static final long PI_O_4_BITS[] = new long[] {<a name="line.277"></a>
<FONT color="green">278</FONT>            (0xc90fdaa2L &lt;&lt; 32) | 0x2168c234L,<a name="line.278"></a>
<FONT color="green">279</FONT>            (0xc4c6628bL &lt;&lt; 32) | 0x80dc1cd1L };<a name="line.279"></a>
<FONT color="green">280</FONT>    <a name="line.280"></a>
<FONT color="green">281</FONT>        /** Eighths.<a name="line.281"></a>
<FONT color="green">282</FONT>         * This is used by sinQ, because its faster to do a table lookup than<a name="line.282"></a>
<FONT color="green">283</FONT>         * a multiply in this time-critical routine<a name="line.283"></a>
<FONT color="green">284</FONT>         */<a name="line.284"></a>
<FONT color="green">285</FONT>        private static final double EIGHTHS[] = {0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0, 1.125, 1.25, 1.375, 1.5, 1.625};<a name="line.285"></a>
<FONT color="green">286</FONT>    <a name="line.286"></a>
<FONT color="green">287</FONT>        /** Table of 2^((n+2)/3) */<a name="line.287"></a>
<FONT color="green">288</FONT>        private static final double CBRTTWO[] = { 0.6299605249474366,<a name="line.288"></a>
<FONT color="green">289</FONT>                                                0.7937005259840998,<a name="line.289"></a>
<FONT color="green">290</FONT>                                                1.0,<a name="line.290"></a>
<FONT color="green">291</FONT>                                                1.2599210498948732,<a name="line.291"></a>
<FONT color="green">292</FONT>                                                1.5874010519681994 };<a name="line.292"></a>
<FONT color="green">293</FONT>    <a name="line.293"></a>
<FONT color="green">294</FONT>        /*<a name="line.294"></a>
<FONT color="green">295</FONT>         *  There are 52 bits in the mantissa of a double.<a name="line.295"></a>
<FONT color="green">296</FONT>         *  For additional precision, the code splits double numbers into two parts,<a name="line.296"></a>
<FONT color="green">297</FONT>         *  by clearing the low order 30 bits if possible, and then performs the arithmetic<a name="line.297"></a>
<FONT color="green">298</FONT>         *  on each half separately.<a name="line.298"></a>
<FONT color="green">299</FONT>         */<a name="line.299"></a>
<FONT color="green">300</FONT>    <a name="line.300"></a>
<FONT color="green">301</FONT>        /**<a name="line.301"></a>
<FONT color="green">302</FONT>         * 0x40000000 - used to split a double into two parts, both with the low order bits cleared.<a name="line.302"></a>
<FONT color="green">303</FONT>         * Equivalent to 2^30.<a name="line.303"></a>
<FONT color="green">304</FONT>         */<a name="line.304"></a>
<FONT color="green">305</FONT>        private static final long HEX_40000000 = 0x40000000L; // 1073741824L<a name="line.305"></a>
<FONT color="green">306</FONT>    <a name="line.306"></a>
<FONT color="green">307</FONT>        /** Mask used to clear low order 30 bits */<a name="line.307"></a>
<FONT color="green">308</FONT>        private static final long MASK_30BITS = -1L - (HEX_40000000 -1); // 0xFFFFFFFFC0000000L;<a name="line.308"></a>
<FONT color="green">309</FONT>    <a name="line.309"></a>
<FONT color="green">310</FONT>        /** 2^52 - double numbers this large must be integral (no fraction) or NaN or Infinite */<a name="line.310"></a>
<FONT color="green">311</FONT>        private static final double TWO_POWER_52 = 4503599627370496.0;<a name="line.311"></a>
<FONT color="green">312</FONT>        /** 2^53 - double numbers this large must be even. */<a name="line.312"></a>
<FONT color="green">313</FONT>        private static final double TWO_POWER_53 = 2 * TWO_POWER_52;<a name="line.313"></a>
<FONT color="green">314</FONT>    <a name="line.314"></a>
<FONT color="green">315</FONT>        /** Constant: {@value}. */<a name="line.315"></a>
<FONT color="green">316</FONT>        private static final double F_1_3 = 1d / 3d;<a name="line.316"></a>
<FONT color="green">317</FONT>        /** Constant: {@value}. */<a name="line.317"></a>
<FONT color="green">318</FONT>        private static final double F_1_5 = 1d / 5d;<a name="line.318"></a>
<FONT color="green">319</FONT>        /** Constant: {@value}. */<a name="line.319"></a>
<FONT color="green">320</FONT>        private static final double F_1_7 = 1d / 7d;<a name="line.320"></a>
<FONT color="green">321</FONT>        /** Constant: {@value}. */<a name="line.321"></a>
<FONT color="green">322</FONT>        private static final double F_1_9 = 1d / 9d;<a name="line.322"></a>
<FONT color="green">323</FONT>        /** Constant: {@value}. */<a name="line.323"></a>
<FONT color="green">324</FONT>        private static final double F_1_11 = 1d / 11d;<a name="line.324"></a>
<FONT color="green">325</FONT>        /** Constant: {@value}. */<a name="line.325"></a>
<FONT color="green">326</FONT>        private static final double F_1_13 = 1d / 13d;<a name="line.326"></a>
<FONT color="green">327</FONT>        /** Constant: {@value}. */<a name="line.327"></a>
<FONT color="green">328</FONT>        private static final double F_1_15 = 1d / 15d;<a name="line.328"></a>
<FONT color="green">329</FONT>        /** Constant: {@value}. */<a name="line.329"></a>
<FONT color="green">330</FONT>        private static final double F_1_17 = 1d / 17d;<a name="line.330"></a>
<FONT color="green">331</FONT>        /** Constant: {@value}. */<a name="line.331"></a>
<FONT color="green">332</FONT>        private static final double F_3_4 = 3d / 4d;<a name="line.332"></a>
<FONT color="green">333</FONT>        /** Constant: {@value}. */<a name="line.333"></a>
<FONT color="green">334</FONT>        private static final double F_15_16 = 15d / 16d;<a name="line.334"></a>
<FONT color="green">335</FONT>        /** Constant: {@value}. */<a name="line.335"></a>
<FONT color="green">336</FONT>        private static final double F_13_14 = 13d / 14d;<a name="line.336"></a>
<FONT color="green">337</FONT>        /** Constant: {@value}. */<a name="line.337"></a>
<FONT color="green">338</FONT>        private static final double F_11_12 = 11d / 12d;<a name="line.338"></a>
<FONT color="green">339</FONT>        /** Constant: {@value}. */<a name="line.339"></a>
<FONT color="green">340</FONT>        private static final double F_9_10 = 9d / 10d;<a name="line.340"></a>
<FONT color="green">341</FONT>        /** Constant: {@value}. */<a name="line.341"></a>
<FONT color="green">342</FONT>        private static final double F_7_8 = 7d / 8d;<a name="line.342"></a>
<FONT color="green">343</FONT>        /** Constant: {@value}. */<a name="line.343"></a>
<FONT color="green">344</FONT>        private static final double F_5_6 = 5d / 6d;<a name="line.344"></a>
<FONT color="green">345</FONT>        /** Constant: {@value}. */<a name="line.345"></a>
<FONT color="green">346</FONT>        private static final double F_1_2 = 1d / 2d;<a name="line.346"></a>
<FONT color="green">347</FONT>        /** Constant: {@value}. */<a name="line.347"></a>
<FONT color="green">348</FONT>        private static final double F_1_4 = 1d / 4d;<a name="line.348"></a>
<FONT color="green">349</FONT>    <a name="line.349"></a>
<FONT color="green">350</FONT>        /**<a name="line.350"></a>
<FONT color="green">351</FONT>         * Private Constructor<a name="line.351"></a>
<FONT color="green">352</FONT>         */<a name="line.352"></a>
<FONT color="green">353</FONT>        private FastMath() {}<a name="line.353"></a>
<FONT color="green">354</FONT>    <a name="line.354"></a>
<FONT color="green">355</FONT>        // Generic helper methods<a name="line.355"></a>
<FONT color="green">356</FONT>    <a name="line.356"></a>
<FONT color="green">357</FONT>        /**<a name="line.357"></a>
<FONT color="green">358</FONT>         * Get the high order bits from the mantissa.<a name="line.358"></a>
<FONT color="green">359</FONT>         * Equivalent to adding and subtracting HEX_40000 but also works for very large numbers<a name="line.359"></a>
<FONT color="green">360</FONT>         *<a name="line.360"></a>
<FONT color="green">361</FONT>         * @param d the value to split<a name="line.361"></a>
<FONT color="green">362</FONT>         * @return the high order part of the mantissa<a name="line.362"></a>
<FONT color="green">363</FONT>         */<a name="line.363"></a>
<FONT color="green">364</FONT>        private static double doubleHighPart(double d) {<a name="line.364"></a>
<FONT color="green">365</FONT>            if (d &gt; -Precision.SAFE_MIN &amp;&amp; d &lt; Precision.SAFE_MIN){<a name="line.365"></a>
<FONT color="green">366</FONT>                return d; // These are un-normalised - don't try to convert<a name="line.366"></a>
<FONT color="green">367</FONT>            }<a name="line.367"></a>
<FONT color="green">368</FONT>            long xl = Double.doubleToLongBits(d);<a name="line.368"></a>
<FONT color="green">369</FONT>            xl = xl &amp; MASK_30BITS; // Drop low order bits<a name="line.369"></a>
<FONT color="green">370</FONT>            return Double.longBitsToDouble(xl);<a name="line.370"></a>
<FONT color="green">371</FONT>        }<a name="line.371"></a>
<FONT color="green">372</FONT>    <a name="line.372"></a>
<FONT color="green">373</FONT>        /** Compute the square root of a number.<a name="line.373"></a>
<FONT color="green">374</FONT>         * &lt;p&gt;&lt;b&gt;Note:&lt;/b&gt; this implementation currently delegates to {@link Math#sqrt}<a name="line.374"></a>
<FONT color="green">375</FONT>         * @param a number on which evaluation is done<a name="line.375"></a>
<FONT color="green">376</FONT>         * @return square root of a<a name="line.376"></a>
<FONT color="green">377</FONT>         */<a name="line.377"></a>
<FONT color="green">378</FONT>        public static double sqrt(final double a) {<a name="line.378"></a>
<FONT color="green">379</FONT>            return Math.sqrt(a);<a name="line.379"></a>
<FONT color="green">380</FONT>        }<a name="line.380"></a>
<FONT color="green">381</FONT>    <a name="line.381"></a>
<FONT color="green">382</FONT>        /** Compute the hyperbolic cosine of a number.<a name="line.382"></a>
<FONT color="green">383</FONT>         * @param x number on which evaluation is done<a name="line.383"></a>
<FONT color="green">384</FONT>         * @return hyperbolic cosine of x<a name="line.384"></a>
<FONT color="green">385</FONT>         */<a name="line.385"></a>
<FONT color="green">386</FONT>        public static double cosh(double x) {<a name="line.386"></a>
<FONT color="green">387</FONT>          if (x != x) {<a name="line.387"></a>
<FONT color="green">388</FONT>              return x;<a name="line.388"></a>
<FONT color="green">389</FONT>          }<a name="line.389"></a>
<FONT color="green">390</FONT>    <a name="line.390"></a>
<FONT color="green">391</FONT>          // cosh[z] = (exp(z) + exp(-z))/2<a name="line.391"></a>
<FONT color="green">392</FONT>    <a name="line.392"></a>
<FONT color="green">393</FONT>          // for numbers with magnitude 20 or so,<a name="line.393"></a>
<FONT color="green">394</FONT>          // exp(-z) can be ignored in comparison with exp(z)<a name="line.394"></a>
<FONT color="green">395</FONT>    <a name="line.395"></a>
<FONT color="green">396</FONT>          if (x &gt; 20) {<a name="line.396"></a>
<FONT color="green">397</FONT>              if (x &gt;= LOG_MAX_VALUE) {<a name="line.397"></a>
<FONT color="green">398</FONT>                  // Avoid overflow (MATH-905).<a name="line.398"></a>
<FONT color="green">399</FONT>                  final double t = exp(0.5 * x);<a name="line.399"></a>
<FONT color="green">400</FONT>                  return (0.5 * t) * t;<a name="line.400"></a>
<FONT color="green">401</FONT>              } else {<a name="line.401"></a>
<FONT color="green">402</FONT>                  return 0.5 * exp(x);<a name="line.402"></a>
<FONT color="green">403</FONT>              }<a name="line.403"></a>
<FONT color="green">404</FONT>          } else if (x &lt; -20) {<a name="line.404"></a>
<FONT color="green">405</FONT>              if (x &lt;= -LOG_MAX_VALUE) {<a name="line.405"></a>
<FONT color="green">406</FONT>                  // Avoid overflow (MATH-905).<a name="line.406"></a>
<FONT color="green">407</FONT>                  final double t = exp(-0.5 * x);<a name="line.407"></a>
<FONT color="green">408</FONT>                  return (0.5 * t) * t;<a name="line.408"></a>
<FONT color="green">409</FONT>              } else {<a name="line.409"></a>
<FONT color="green">410</FONT>                  return 0.5 * exp(-x);<a name="line.410"></a>
<FONT color="green">411</FONT>              }<a name="line.411"></a>
<FONT color="green">412</FONT>          }<a name="line.412"></a>
<FONT color="green">413</FONT>    <a name="line.413"></a>
<FONT color="green">414</FONT>          final double hiPrec[] = new double[2];<a name="line.414"></a>
<FONT color="green">415</FONT>          if (x &lt; 0.0) {<a name="line.415"></a>
<FONT color="green">416</FONT>              x = -x;<a name="line.416"></a>
<FONT color="green">417</FONT>          }<a name="line.417"></a>
<FONT color="green">418</FONT>          exp(x, 0.0, hiPrec);<a name="line.418"></a>
<FONT color="green">419</FONT>    <a name="line.419"></a>
<FONT color="green">420</FONT>          double ya = hiPrec[0] + hiPrec[1];<a name="line.420"></a>
<FONT color="green">421</FONT>          double yb = -(ya - hiPrec[0] - hiPrec[1]);<a name="line.421"></a>
<FONT color="green">422</FONT>    <a name="line.422"></a>
<FONT color="green">423</FONT>          double temp = ya * HEX_40000000;<a name="line.423"></a>
<FONT color="green">424</FONT>          double yaa = ya + temp - temp;<a name="line.424"></a>
<FONT color="green">425</FONT>          double yab = ya - yaa;<a name="line.425"></a>
<FONT color="green">426</FONT>    <a name="line.426"></a>
<FONT color="green">427</FONT>          // recip = 1/y<a name="line.427"></a>
<FONT color="green">428</FONT>          double recip = 1.0/ya;<a name="line.428"></a>
<FONT color="green">429</FONT>          temp = recip * HEX_40000000;<a name="line.429"></a>
<FONT color="green">430</FONT>          double recipa = recip + temp - temp;<a name="line.430"></a>
<FONT color="green">431</FONT>          double recipb = recip - recipa;<a name="line.431"></a>
<FONT color="green">432</FONT>    <a name="line.432"></a>
<FONT color="green">433</FONT>          // Correct for rounding in division<a name="line.433"></a>
<FONT color="green">434</FONT>          recipb += (1.0 - yaa*recipa - yaa*recipb - yab*recipa - yab*recipb) * recip;<a name="line.434"></a>
<FONT color="green">435</FONT>          // Account for yb<a name="line.435"></a>
<FONT color="green">436</FONT>          recipb += -yb * recip * recip;<a name="line.436"></a>
<FONT color="green">437</FONT>    <a name="line.437"></a>
<FONT color="green">438</FONT>          // y = y + 1/y<a name="line.438"></a>
<FONT color="green">439</FONT>          temp = ya + recipa;<a name="line.439"></a>
<FONT color="green">440</FONT>          yb += -(temp - ya - recipa);<a name="line.440"></a>
<FONT color="green">441</FONT>          ya = temp;<a name="line.441"></a>
<FONT color="green">442</FONT>          temp = ya + recipb;<a name="line.442"></a>
<FONT color="green">443</FONT>          yb += -(temp - ya - recipb);<a name="line.443"></a>
<FONT color="green">444</FONT>          ya = temp;<a name="line.444"></a>
<FONT color="green">445</FONT>    <a name="line.445"></a>
<FONT color="green">446</FONT>          double result = ya + yb;<a name="line.446"></a>
<FONT color="green">447</FONT>          result *= 0.5;<a name="line.447"></a>
<FONT color="green">448</FONT>          return result;<a name="line.448"></a>
<FONT color="green">449</FONT>        }<a name="line.449"></a>
<FONT color="green">450</FONT>    <a name="line.450"></a>
<FONT color="green">451</FONT>        /** Compute the hyperbolic sine of a number.<a name="line.451"></a>
<FONT color="green">452</FONT>         * @param x number on which evaluation is done<a name="line.452"></a>
<FONT color="green">453</FONT>         * @return hyperbolic sine of x<a name="line.453"></a>
<FONT color="green">454</FONT>         */<a name="line.454"></a>
<FONT color="green">455</FONT>        public static double sinh(double x) {<a name="line.455"></a>
<FONT color="green">456</FONT>          boolean negate = false;<a name="line.456"></a>
<FONT color="green">457</FONT>          if (x != x) {<a name="line.457"></a>
<FONT color="green">458</FONT>              return x;<a name="line.458"></a>
<FONT color="green">459</FONT>          }<a name="line.459"></a>
<FONT color="green">460</FONT>    <a name="line.460"></a>
<FONT color="green">461</FONT>          // sinh[z] = (exp(z) - exp(-z) / 2<a name="line.461"></a>
<FONT color="green">462</FONT>    <a name="line.462"></a>
<FONT color="green">463</FONT>          // for values of z larger than about 20,<a name="line.463"></a>
<FONT color="green">464</FONT>          // exp(-z) can be ignored in comparison with exp(z)<a name="line.464"></a>
<FONT color="green">465</FONT>    <a name="line.465"></a>
<FONT color="green">466</FONT>          if (x &gt; 20) {<a name="line.466"></a>
<FONT color="green">467</FONT>              if (x &gt;= LOG_MAX_VALUE) {<a name="line.467"></a>
<FONT color="green">468</FONT>                  // Avoid overflow (MATH-905).<a name="line.468"></a>
<FONT color="green">469</FONT>                  final double t = exp(0.5 * x);<a name="line.469"></a>
<FONT color="green">470</FONT>                  return (0.5 * t) * t;<a name="line.470"></a>
<FONT color="green">471</FONT>              } else {<a name="line.471"></a>
<FONT color="green">472</FONT>                  return 0.5 * exp(x);<a name="line.472"></a>
<FONT color="green">473</FONT>              }<a name="line.473"></a>
<FONT color="green">474</FONT>          } else if (x &lt; -20) {<a name="line.474"></a>
<FONT color="green">475</FONT>              if (x &lt;= -LOG_MAX_VALUE) {<a name="line.475"></a>
<FONT color="green">476</FONT>                  // Avoid overflow (MATH-905).<a name="line.476"></a>
<FONT color="green">477</FONT>                  final double t = exp(-0.5 * x);<a name="line.477"></a>
<FONT color="green">478</FONT>                  return (-0.5 * t) * t;<a name="line.478"></a>
<FONT color="green">479</FONT>              } else {<a name="line.479"></a>
<FONT color="green">480</FONT>                  return -0.5 * exp(-x);<a name="line.480"></a>
<FONT color="green">481</FONT>              }<a name="line.481"></a>
<FONT color="green">482</FONT>          }<a name="line.482"></a>
<FONT color="green">483</FONT>    <a name="line.483"></a>
<FONT color="green">484</FONT>          if (x == 0) {<a name="line.484"></a>
<FONT color="green">485</FONT>              return x;<a name="line.485"></a>
<FONT color="green">486</FONT>          }<a name="line.486"></a>
<FONT color="green">487</FONT>    <a name="line.487"></a>
<FONT color="green">488</FONT>          if (x &lt; 0.0) {<a name="line.488"></a>
<FONT color="green">489</FONT>              x = -x;<a name="line.489"></a>
<FONT color="green">490</FONT>              negate = true;<a name="line.490"></a>
<FONT color="green">491</FONT>          }<a name="line.491"></a>
<FONT color="green">492</FONT>    <a name="line.492"></a>
<FONT color="green">493</FONT>          double result;<a name="line.493"></a>
<FONT color="green">494</FONT>    <a name="line.494"></a>
<FONT color="green">495</FONT>          if (x &gt; 0.25) {<a name="line.495"></a>
<FONT color="green">496</FONT>              double hiPrec[] = new double[2];<a name="line.496"></a>
<FONT color="green">497</FONT>              exp(x, 0.0, hiPrec);<a name="line.497"></a>
<FONT color="green">498</FONT>    <a name="line.498"></a>
<FONT color="green">499</FONT>              double ya = hiPrec[0] + hiPrec[1];<a name="line.499"></a>
<FONT color="green">500</FONT>              double yb = -(ya - hiPrec[0] - hiPrec[1]);<a name="line.500"></a>
<FONT color="green">501</FONT>    <a name="line.501"></a>
<FONT color="green">502</FONT>              double temp = ya * HEX_40000000;<a name="line.502"></a>
<FONT color="green">503</FONT>              double yaa = ya + temp - temp;<a name="line.503"></a>
<FONT color="green">504</FONT>              double yab = ya - yaa;<a name="line.504"></a>
<FONT color="green">505</FONT>    <a name="line.505"></a>
<FONT color="green">506</FONT>              // recip = 1/y<a name="line.506"></a>
<FONT color="green">507</FONT>              double recip = 1.0/ya;<a name="line.507"></a>
<FONT color="green">508</FONT>              temp = recip * HEX_40000000;<a name="line.508"></a>
<FONT color="green">509</FONT>              double recipa = recip + temp - temp;<a name="line.509"></a>
<FONT color="green">510</FONT>              double recipb = recip - recipa;<a name="line.510"></a>
<FONT color="green">511</FONT>    <a name="line.511"></a>
<FONT color="green">512</FONT>              // Correct for rounding in division<a name="line.512"></a>
<FONT color="green">513</FONT>              recipb += (1.0 - yaa*recipa - yaa*recipb - yab*recipa - yab*recipb) * recip;<a name="line.513"></a>
<FONT color="green">514</FONT>              // Account for yb<a name="line.514"></a>
<FONT color="green">515</FONT>              recipb += -yb * recip * recip;<a name="line.515"></a>
<FONT color="green">516</FONT>    <a name="line.516"></a>
<FONT color="green">517</FONT>              recipa = -recipa;<a name="line.517"></a>
<FONT color="green">518</FONT>              recipb = -recipb;<a name="line.518"></a>
<FONT color="green">519</FONT>    <a name="line.519"></a>
<FONT color="green">520</FONT>              // y = y + 1/y<a name="line.520"></a>
<FONT color="green">521</FONT>              temp = ya + recipa;<a name="line.521"></a>
<FONT color="green">522</FONT>              yb += -(temp - ya - recipa);<a name="line.522"></a>
<FONT color="green">523</FONT>              ya = temp;<a name="line.523"></a>
<FONT color="green">524</FONT>              temp = ya + recipb;<a name="line.524"></a>
<FONT color="green">525</FONT>              yb += -(temp - ya - recipb);<a name="line.525"></a>
<FONT color="green">526</FONT>              ya = temp;<a name="line.526"></a>
<FONT color="green">527</FONT>    <a name="line.527"></a>
<FONT color="green">528</FONT>              result = ya + yb;<a name="line.528"></a>
<FONT color="green">529</FONT>              result *= 0.5;<a name="line.529"></a>
<FONT color="green">530</FONT>          }<a name="line.530"></a>
<FONT color="green">531</FONT>          else {<a name="line.531"></a>
<FONT color="green">532</FONT>              double hiPrec[] = new double[2];<a name="line.532"></a>
<FONT color="green">533</FONT>              expm1(x, hiPrec);<a name="line.533"></a>
<FONT color="green">534</FONT>    <a name="line.534"></a>
<FONT color="green">535</FONT>              double ya = hiPrec[0] + hiPrec[1];<a name="line.535"></a>
<FONT color="green">536</FONT>              double yb = -(ya - hiPrec[0] - hiPrec[1]);<a name="line.536"></a>
<FONT color="green">537</FONT>    <a name="line.537"></a>
<FONT color="green">538</FONT>              /* Compute expm1(-x) = -expm1(x) / (expm1(x) + 1) */<a name="line.538"></a>
<FONT color="green">539</FONT>              double denom = 1.0 + ya;<a name="line.539"></a>
<FONT color="green">540</FONT>              double denomr = 1.0 / denom;<a name="line.540"></a>
<FONT color="green">541</FONT>              double denomb = -(denom - 1.0 - ya) + yb;<a name="line.541"></a>
<FONT color="green">542</FONT>              double ratio = ya * denomr;<a name="line.542"></a>
<FONT color="green">543</FONT>              double temp = ratio * HEX_40000000;<a name="line.543"></a>
<FONT color="green">544</FONT>              double ra = ratio + temp - temp;<a name="line.544"></a>
<FONT color="green">545</FONT>              double rb = ratio - ra;<a name="line.545"></a>
<FONT color="green">546</FONT>    <a name="line.546"></a>
<FONT color="green">547</FONT>              temp = denom * HEX_40000000;<a name="line.547"></a>
<FONT color="green">548</FONT>              double za = denom + temp - temp;<a name="line.548"></a>
<FONT color="green">549</FONT>              double zb = denom - za;<a name="line.549"></a>
<FONT color="green">550</FONT>    <a name="line.550"></a>
<FONT color="green">551</FONT>              rb += (ya - za*ra - za*rb - zb*ra - zb*rb) * denomr;<a name="line.551"></a>
<FONT color="green">552</FONT>    <a name="line.552"></a>
<FONT color="green">553</FONT>              // Adjust for yb<a name="line.553"></a>
<FONT color="green">554</FONT>              rb += yb*denomr;                        // numerator<a name="line.554"></a>
<FONT color="green">555</FONT>              rb += -ya * denomb * denomr * denomr;   // denominator<a name="line.555"></a>
<FONT color="green">556</FONT>    <a name="line.556"></a>
<FONT color="green">557</FONT>              // y = y - 1/y<a name="line.557"></a>
<FONT color="green">558</FONT>              temp = ya + ra;<a name="line.558"></a>
<FONT color="green">559</FONT>              yb += -(temp - ya - ra);<a name="line.559"></a>
<FONT color="green">560</FONT>              ya = temp;<a name="line.560"></a>
<FONT color="green">561</FONT>              temp = ya + rb;<a name="line.561"></a>
<FONT color="green">562</FONT>              yb += -(temp - ya - rb);<a name="line.562"></a>
<FONT color="green">563</FONT>              ya = temp;<a name="line.563"></a>
<FONT color="green">564</FONT>    <a name="line.564"></a>
<FONT color="green">565</FONT>              result = ya + yb;<a name="line.565"></a>
<FONT color="green">566</FONT>              result *= 0.5;<a name="line.566"></a>
<FONT color="green">567</FONT>          }<a name="line.567"></a>
<FONT color="green">568</FONT>    <a name="line.568"></a>
<FONT color="green">569</FONT>          if (negate) {<a name="line.569"></a>
<FONT color="green">570</FONT>              result = -result;<a name="line.570"></a>
<FONT color="green">571</FONT>          }<a name="line.571"></a>
<FONT color="green">572</FONT>    <a name="line.572"></a>
<FONT color="green">573</FONT>          return result;<a name="line.573"></a>
<FONT color="green">574</FONT>        }<a name="line.574"></a>
<FONT color="green">575</FONT>    <a name="line.575"></a>
<FONT color="green">576</FONT>        /** Compute the hyperbolic tangent of a number.<a name="line.576"></a>
<FONT color="green">577</FONT>         * @param x number on which evaluation is done<a name="line.577"></a>
<FONT color="green">578</FONT>         * @return hyperbolic tangent of x<a name="line.578"></a>
<FONT color="green">579</FONT>         */<a name="line.579"></a>
<FONT color="green">580</FONT>        public static double tanh(double x) {<a name="line.580"></a>
<FONT color="green">581</FONT>          boolean negate = false;<a name="line.581"></a>
<FONT color="green">582</FONT>    <a name="line.582"></a>
<FONT color="green">583</FONT>          if (x != x) {<a name="line.583"></a>
<FONT color="green">584</FONT>              return x;<a name="line.584"></a>
<FONT color="green">585</FONT>          }<a name="line.585"></a>
<FONT color="green">586</FONT>    <a name="line.586"></a>
<FONT color="green">587</FONT>          // tanh[z] = sinh[z] / cosh[z]<a name="line.587"></a>
<FONT color="green">588</FONT>          // = (exp(z) - exp(-z)) / (exp(z) + exp(-z))<a name="line.588"></a>
<FONT color="green">589</FONT>          // = (exp(2x) - 1) / (exp(2x) + 1)<a name="line.589"></a>
<FONT color="green">590</FONT>    <a name="line.590"></a>
<FONT color="green">591</FONT>          // for magnitude &gt; 20, sinh[z] == cosh[z] in double precision<a name="line.591"></a>
<FONT color="green">592</FONT>    <a name="line.592"></a>
<FONT color="green">593</FONT>          if (x &gt; 20.0) {<a name="line.593"></a>
<FONT color="green">594</FONT>              return 1.0;<a name="line.594"></a>
<FONT color="green">595</FONT>          }<a name="line.595"></a>
<FONT color="green">596</FONT>    <a name="line.596"></a>
<FONT color="green">597</FONT>          if (x &lt; -20) {<a name="line.597"></a>
<FONT color="green">598</FONT>              return -1.0;<a name="line.598"></a>
<FONT color="green">599</FONT>          }<a name="line.599"></a>
<FONT color="green">600</FONT>    <a name="line.600"></a>
<FONT color="green">601</FONT>          if (x == 0) {<a name="line.601"></a>
<FONT color="green">602</FONT>              return x;<a name="line.602"></a>
<FONT color="green">603</FONT>          }<a name="line.603"></a>
<FONT color="green">604</FONT>    <a name="line.604"></a>
<FONT color="green">605</FONT>          if (x &lt; 0.0) {<a name="line.605"></a>
<FONT color="green">606</FONT>              x = -x;<a name="line.606"></a>
<FONT color="green">607</FONT>              negate = true;<a name="line.607"></a>
<FONT color="green">608</FONT>          }<a name="line.608"></a>
<FONT color="green">609</FONT>    <a name="line.609"></a>
<FONT color="green">610</FONT>          double result;<a name="line.610"></a>
<FONT color="green">611</FONT>          if (x &gt;= 0.5) {<a name="line.611"></a>
<FONT color="green">612</FONT>              double hiPrec[] = new double[2];<a name="line.612"></a>
<FONT color="green">613</FONT>              // tanh(x) = (exp(2x) - 1) / (exp(2x) + 1)<a name="line.613"></a>
<FONT color="green">614</FONT>              exp(x*2.0, 0.0, hiPrec);<a name="line.614"></a>
<FONT color="green">615</FONT>    <a name="line.615"></a>
<FONT color="green">616</FONT>              double ya = hiPrec[0] + hiPrec[1];<a name="line.616"></a>
<FONT color="green">617</FONT>              double yb = -(ya - hiPrec[0] - hiPrec[1]);<a name="line.617"></a>
<FONT color="green">618</FONT>    <a name="line.618"></a>
<FONT color="green">619</FONT>              /* Numerator */<a name="line.619"></a>
<FONT color="green">620</FONT>              double na = -1.0 + ya;<a name="line.620"></a>
<FONT color="green">621</FONT>              double nb = -(na + 1.0 - ya);<a name="line.621"></a>
<FONT color="green">622</FONT>              double temp = na + yb;<a name="line.622"></a>
<FONT color="green">623</FONT>              nb += -(temp - na - yb);<a name="line.623"></a>
<FONT color="green">624</FONT>              na = temp;<a name="line.624"></a>
<FONT color="green">625</FONT>    <a name="line.625"></a>
<FONT color="green">626</FONT>              /* Denominator */<a name="line.626"></a>
<FONT color="green">627</FONT>              double da = 1.0 + ya;<a name="line.627"></a>
<FONT color="green">628</FONT>              double db = -(da - 1.0 - ya);<a name="line.628"></a>
<FONT color="green">629</FONT>              temp = da + yb;<a name="line.629"></a>
<FONT color="green">630</FONT>              db += -(temp - da - yb);<a name="line.630"></a>
<FONT color="green">631</FONT>              da = temp;<a name="line.631"></a>
<FONT color="green">632</FONT>    <a name="line.632"></a>
<FONT color="green">633</FONT>              temp = da * HEX_40000000;<a name="line.633"></a>
<FONT color="green">634</FONT>              double daa = da + temp - temp;<a name="line.634"></a>
<FONT color="green">635</FONT>              double dab = da - daa;<a name="line.635"></a>
<FONT color="green">636</FONT>    <a name="line.636"></a>
<FONT color="green">637</FONT>              // ratio = na/da<a name="line.637"></a>
<FONT color="green">638</FONT>              double ratio = na/da;<a name="line.638"></a>
<FONT color="green">639</FONT>              temp = ratio * HEX_40000000;<a name="line.639"></a>
<FONT color="green">640</FONT>              double ratioa = ratio + temp - temp;<a name="line.640"></a>
<FONT color="green">641</FONT>              double ratiob = ratio - ratioa;<a name="line.641"></a>
<FONT color="green">642</FONT>    <a name="line.642"></a>
<FONT color="green">643</FONT>              // Correct for rounding in division<a name="line.643"></a>
<FONT color="green">644</FONT>              ratiob += (na - daa*ratioa - daa*ratiob - dab*ratioa - dab*ratiob) / da;<a name="line.644"></a>
<FONT color="green">645</FONT>    <a name="line.645"></a>
<FONT color="green">646</FONT>              // Account for nb<a name="line.646"></a>
<FONT color="green">647</FONT>              ratiob += nb / da;<a name="line.647"></a>
<FONT color="green">648</FONT>              // Account for db<a name="line.648"></a>
<FONT color="green">649</FONT>              ratiob += -db * na / da / da;<a name="line.649"></a>
<FONT color="green">650</FONT>    <a name="line.650"></a>
<FONT color="green">651</FONT>              result = ratioa + ratiob;<a name="line.651"></a>
<FONT color="green">652</FONT>          }<a name="line.652"></a>
<FONT color="green">653</FONT>          else {<a name="line.653"></a>
<FONT color="green">654</FONT>              double hiPrec[] = new double[2];<a name="line.654"></a>
<FONT color="green">655</FONT>              // tanh(x) = expm1(2x) / (expm1(2x) + 2)<a name="line.655"></a>
<FONT color="green">656</FONT>              expm1(x*2.0, hiPrec);<a name="line.656"></a>
<FONT color="green">657</FONT>    <a name="line.657"></a>
<FONT color="green">658</FONT>              double ya = hiPrec[0] + hiPrec[1];<a name="line.658"></a>
<FONT color="green">659</FONT>              double yb = -(ya - hiPrec[0] - hiPrec[1]);<a name="line.659"></a>
<FONT color="green">660</FONT>    <a name="line.660"></a>
<FONT color="green">661</FONT>              /* Numerator */<a name="line.661"></a>
<FONT color="green">662</FONT>              double na = ya;<a name="line.662"></a>
<FONT color="green">663</FONT>              double nb = yb;<a name="line.663"></a>
<FONT color="green">664</FONT>    <a name="line.664"></a>
<FONT color="green">665</FONT>              /* Denominator */<a name="line.665"></a>
<FONT color="green">666</FONT>              double da = 2.0 + ya;<a name="line.666"></a>
<FONT color="green">667</FONT>              double db = -(da - 2.0 - ya);<a name="line.667"></a>
<FONT color="green">668</FONT>              double temp = da + yb;<a name="line.668"></a>
<FONT color="green">669</FONT>              db += -(temp - da - yb);<a name="line.669"></a>
<FONT color="green">670</FONT>              da = temp;<a name="line.670"></a>
<FONT color="green">671</FONT>    <a name="line.671"></a>
<FONT color="green">672</FONT>              temp = da * HEX_40000000;<a name="line.672"></a>
<FONT color="green">673</FONT>              double daa = da + temp - temp;<a name="line.673"></a>
<FONT color="green">674</FONT>              double dab = da - daa;<a name="line.674"></a>
<FONT color="green">675</FONT>    <a name="line.675"></a>
<FONT color="green">676</FONT>              // ratio = na/da<a name="line.676"></a>
<FONT color="green">677</FONT>              double ratio = na/da;<a name="line.677"></a>
<FONT color="green">678</FONT>              temp = ratio * HEX_40000000;<a name="line.678"></a>
<FONT color="green">679</FONT>              double ratioa = ratio + temp - temp;<a name="line.679"></a>
<FONT color="green">680</FONT>              double ratiob = ratio - ratioa;<a name="line.680"></a>
<FONT color="green">681</FONT>    <a name="line.681"></a>
<FONT color="green">682</FONT>              // Correct for rounding in division<a name="line.682"></a>
<FONT color="green">683</FONT>              ratiob += (na - daa*ratioa - daa*ratiob - dab*ratioa - dab*ratiob) / da;<a name="line.683"></a>
<FONT color="green">684</FONT>    <a name="line.684"></a>
<FONT color="green">685</FONT>              // Account for nb<a name="line.685"></a>
<FONT color="green">686</FONT>              ratiob += nb / da;<a name="line.686"></a>
<FONT color="green">687</FONT>              // Account for db<a name="line.687"></a>
<FONT color="green">688</FONT>              ratiob += -db * na / da / da;<a name="line.688"></a>
<FONT color="green">689</FONT>    <a name="line.689"></a>
<FONT color="green">690</FONT>              result = ratioa + ratiob;<a name="line.690"></a>
<FONT color="green">691</FONT>          }<a name="line.691"></a>
<FONT color="green">692</FONT>    <a name="line.692"></a>
<FONT color="green">693</FONT>          if (negate) {<a name="line.693"></a>
<FONT color="green">694</FONT>              result = -result;<a name="line.694"></a>
<FONT color="green">695</FONT>          }<a name="line.695"></a>
<FONT color="green">696</FONT>    <a name="line.696"></a>
<FONT color="green">697</FONT>          return result;<a name="line.697"></a>
<FONT color="green">698</FONT>        }<a name="line.698"></a>
<FONT color="green">699</FONT>    <a name="line.699"></a>
<FONT color="green">700</FONT>        /** Compute the inverse hyperbolic cosine of a number.<a name="line.700"></a>
<FONT color="green">701</FONT>         * @param a number on which evaluation is done<a name="line.701"></a>
<FONT color="green">702</FONT>         * @return inverse hyperbolic cosine of a<a name="line.702"></a>
<FONT color="green">703</FONT>         */<a name="line.703"></a>
<FONT color="green">704</FONT>        public static double acosh(final double a) {<a name="line.704"></a>
<FONT color="green">705</FONT>            return FastMath.log(a + FastMath.sqrt(a * a - 1));<a name="line.705"></a>
<FONT color="green">706</FONT>        }<a name="line.706"></a>
<FONT color="green">707</FONT>    <a name="line.707"></a>
<FONT color="green">708</FONT>        /** Compute the inverse hyperbolic sine of a number.<a name="line.708"></a>
<FONT color="green">709</FONT>         * @param a number on which evaluation is done<a name="line.709"></a>
<FONT color="green">710</FONT>         * @return inverse hyperbolic sine of a<a name="line.710"></a>
<FONT color="green">711</FONT>         */<a name="line.711"></a>
<FONT color="green">712</FONT>        public static double asinh(double a) {<a name="line.712"></a>
<FONT color="green">713</FONT>            boolean negative = false;<a name="line.713"></a>
<FONT color="green">714</FONT>            if (a &lt; 0) {<a name="line.714"></a>
<FONT color="green">715</FONT>                negative = true;<a name="line.715"></a>
<FONT color="green">716</FONT>                a = -a;<a name="line.716"></a>
<FONT color="green">717</FONT>            }<a name="line.717"></a>
<FONT color="green">718</FONT>    <a name="line.718"></a>
<FONT color="green">719</FONT>            double absAsinh;<a name="line.719"></a>
<FONT color="green">720</FONT>            if (a &gt; 0.167) {<a name="line.720"></a>
<FONT color="green">721</FONT>                absAsinh = FastMath.log(FastMath.sqrt(a * a + 1) + a);<a name="line.721"></a>
<FONT color="green">722</FONT>            } else {<a name="line.722"></a>
<FONT color="green">723</FONT>                final double a2 = a * a;<a name="line.723"></a>
<FONT color="green">724</FONT>                if (a &gt; 0.097) {<a name="line.724"></a>
<FONT color="green">725</FONT>                    absAsinh = a * (1 - a2 * (F_1_3 - a2 * (F_1_5 - a2 * (F_1_7 - a2 * (F_1_9 - a2 * (F_1_11 - a2 * (F_1_13 - a2 * (F_1_15 - a2 * F_1_17 * F_15_16) * F_13_14) * F_11_12) * F_9_10) * F_7_8) * F_5_6) * F_3_4) * F_1_2);<a name="line.725"></a>
<FONT color="green">726</FONT>                } else if (a &gt; 0.036) {<a name="line.726"></a>
<FONT color="green">727</FONT>                    absAsinh = a * (1 - a2 * (F_1_3 - a2 * (F_1_5 - a2 * (F_1_7 - a2 * (F_1_9 - a2 * (F_1_11 - a2 * F_1_13 * F_11_12) * F_9_10) * F_7_8) * F_5_6) * F_3_4) * F_1_2);<a name="line.727"></a>
<FONT color="green">728</FONT>                } else if (a &gt; 0.0036) {<a name="line.728"></a>
<FONT color="green">729</FONT>                    absAsinh = a * (1 - a2 * (F_1_3 - a2 * (F_1_5 - a2 * (F_1_7 - a2 * F_1_9 * F_7_8) * F_5_6) * F_3_4) * F_1_2);<a name="line.729"></a>
<FONT color="green">730</FONT>                } else {<a name="line.730"></a>
<FONT color="green">731</FONT>                    absAsinh = a * (1 - a2 * (F_1_3 - a2 * F_1_5 * F_3_4) * F_1_2);<a name="line.731"></a>
<FONT color="green">732</FONT>                }<a name="line.732"></a>
<FONT color="green">733</FONT>            }<a name="line.733"></a>
<FONT color="green">734</FONT>    <a name="line.734"></a>
<FONT color="green">735</FONT>            return negative ? -absAsinh : absAsinh;<a name="line.735"></a>
<FONT color="green">736</FONT>        }<a name="line.736"></a>
<FONT color="green">737</FONT>    <a name="line.737"></a>
<FONT color="green">738</FONT>        /** Compute the inverse hyperbolic tangent of a number.<a name="line.738"></a>
<FONT color="green">739</FONT>         * @param a number on which evaluation is done<a name="line.739"></a>
<FONT color="green">740</FONT>         * @return inverse hyperbolic tangent of a<a name="line.740"></a>
<FONT color="green">741</FONT>         */<a name="line.741"></a>
<FONT color="green">742</FONT>        public static double atanh(double a) {<a name="line.742"></a>
<FONT color="green">743</FONT>            boolean negative = false;<a name="line.743"></a>
<FONT color="green">744</FONT>            if (a &lt; 0) {<a name="line.744"></a>
<FONT color="green">745</FONT>                negative = true;<a name="line.745"></a>
<FONT color="green">746</FONT>                a = -a;<a name="line.746"></a>
<FONT color="green">747</FONT>            }<a name="line.747"></a>
<FONT color="green">748</FONT>    <a name="line.748"></a>
<FONT color="green">749</FONT>            double absAtanh;<a name="line.749"></a>
<FONT color="green">750</FONT>            if (a &gt; 0.15) {<a name="line.750"></a>
<FONT color="green">751</FONT>                absAtanh = 0.5 * FastMath.log((1 + a) / (1 - a));<a name="line.751"></a>
<FONT color="green">752</FONT>            } else {<a name="line.752"></a>
<FONT color="green">753</FONT>                final double a2 = a * a;<a name="line.753"></a>
<FONT color="green">754</FONT>                if (a &gt; 0.087) {<a name="line.754"></a>
<FONT color="green">755</FONT>                    absAtanh = a * (1 + a2 * (F_1_3 + a2 * (F_1_5 + a2 * (F_1_7 + a2 * (F_1_9 + a2 * (F_1_11 + a2 * (F_1_13 + a2 * (F_1_15 + a2 * F_1_17))))))));<a name="line.755"></a>
<FONT color="green">756</FONT>                } else if (a &gt; 0.031) {<a name="line.756"></a>
<FONT color="green">757</FONT>                    absAtanh = a * (1 + a2 * (F_1_3 + a2 * (F_1_5 + a2 * (F_1_7 + a2 * (F_1_9 + a2 * (F_1_11 + a2 * F_1_13))))));<a name="line.757"></a>
<FONT color="green">758</FONT>                } else if (a &gt; 0.003) {<a name="line.758"></a>
<FONT color="green">759</FONT>                    absAtanh = a * (1 + a2 * (F_1_3 + a2 * (F_1_5 + a2 * (F_1_7 + a2 * F_1_9))));<a name="line.759"></a>
<FONT color="green">760</FONT>                } else {<a name="line.760"></a>
<FONT color="green">761</FONT>                    absAtanh = a * (1 + a2 * (F_1_3 + a2 * F_1_5));<a name="line.761"></a>
<FONT color="green">762</FONT>                }<a name="line.762"></a>
<FONT color="green">763</FONT>            }<a name="line.763"></a>
<FONT color="green">764</FONT>    <a name="line.764"></a>
<FONT color="green">765</FONT>            return negative ? -absAtanh : absAtanh;<a name="line.765"></a>
<FONT color="green">766</FONT>        }<a name="line.766"></a>
<FONT color="green">767</FONT>    <a name="line.767"></a>
<FONT color="green">768</FONT>        /** Compute the signum of a number.<a name="line.768"></a>
<FONT color="green">769</FONT>         * The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise<a name="line.769"></a>
<FONT color="green">770</FONT>         * @param a number on which evaluation is done<a name="line.770"></a>
<FONT color="green">771</FONT>         * @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a<a name="line.771"></a>
<FONT color="green">772</FONT>         */<a name="line.772"></a>
<FONT color="green">773</FONT>        public static double signum(final double a) {<a name="line.773"></a>
<FONT color="green">774</FONT>            return (a &lt; 0.0) ? -1.0 : ((a &gt; 0.0) ? 1.0 : a); // return +0.0/-0.0/NaN depending on a<a name="line.774"></a>
<FONT color="green">775</FONT>        }<a name="line.775"></a>
<FONT color="green">776</FONT>    <a name="line.776"></a>
<FONT color="green">777</FONT>        /** Compute the signum of a number.<a name="line.777"></a>
<FONT color="green">778</FONT>         * The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise<a name="line.778"></a>
<FONT color="green">779</FONT>         * @param a number on which evaluation is done<a name="line.779"></a>
<FONT color="green">780</FONT>         * @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a<a name="line.780"></a>
<FONT color="green">781</FONT>         */<a name="line.781"></a>
<FONT color="green">782</FONT>        public static float signum(final float a) {<a name="line.782"></a>
<FONT color="green">783</FONT>            return (a &lt; 0.0f) ? -1.0f : ((a &gt; 0.0f) ? 1.0f : a); // return +0.0/-0.0/NaN depending on a<a name="line.783"></a>
<FONT color="green">784</FONT>        }<a name="line.784"></a>
<FONT color="green">785</FONT>    <a name="line.785"></a>
<FONT color="green">786</FONT>        /** Compute next number towards positive infinity.<a name="line.786"></a>
<FONT color="green">787</FONT>         * @param a number to which neighbor should be computed<a name="line.787"></a>
<FONT color="green">788</FONT>         * @return neighbor of a towards positive infinity<a name="line.788"></a>
<FONT color="green">789</FONT>         */<a name="line.789"></a>
<FONT color="green">790</FONT>        public static double nextUp(final double a) {<a name="line.790"></a>
<FONT color="green">791</FONT>            return nextAfter(a, Double.POSITIVE_INFINITY);<a name="line.791"></a>
<FONT color="green">792</FONT>        }<a name="line.792"></a>
<FONT color="green">793</FONT>    <a name="line.793"></a>
<FONT color="green">794</FONT>        /** Compute next number towards positive infinity.<a name="line.794"></a>
<FONT color="green">795</FONT>         * @param a number to which neighbor should be computed<a name="line.795"></a>
<FONT color="green">796</FONT>         * @return neighbor of a towards positive infinity<a name="line.796"></a>
<FONT color="green">797</FONT>         */<a name="line.797"></a>
<FONT color="green">798</FONT>        public static float nextUp(final float a) {<a name="line.798"></a>
<FONT color="green">799</FONT>            return nextAfter(a, Float.POSITIVE_INFINITY);<a name="line.799"></a>
<FONT color="green">800</FONT>        }<a name="line.800"></a>
<FONT color="green">801</FONT>    <a name="line.801"></a>
<FONT color="green">802</FONT>        /** Returns a pseudo-random number between 0.0 and 1.0.<a name="line.802"></a>
<FONT color="green">803</FONT>         * &lt;p&gt;&lt;b&gt;Note:&lt;/b&gt; this implementation currently delegates to {@link Math#random}<a name="line.803"></a>
<FONT color="green">804</FONT>         * @return a random number between 0.0 and 1.0<a name="line.804"></a>
<FONT color="green">805</FONT>         */<a name="line.805"></a>
<FONT color="green">806</FONT>        public static double random() {<a name="line.806"></a>
<FONT color="green">807</FONT>            return Math.random();<a name="line.807"></a>
<FONT color="green">808</FONT>        }<a name="line.808"></a>
<FONT color="green">809</FONT>    <a name="line.809"></a>
<FONT color="green">810</FONT>        /**<a name="line.810"></a>
<FONT color="green">811</FONT>         * Exponential function.<a name="line.811"></a>
<FONT color="green">812</FONT>         *<a name="line.812"></a>
<FONT color="green">813</FONT>         * Computes exp(x), function result is nearly rounded.   It will be correctly<a name="line.813"></a>
<FONT color="green">814</FONT>         * rounded to the theoretical value for 99.9% of input values, otherwise it will<a name="line.814"></a>
<FONT color="green">815</FONT>         * have a 1 UPL error.<a name="line.815"></a>
<FONT color="green">816</FONT>         *<a name="line.816"></a>
<FONT color="green">817</FONT>         * Method:<a name="line.817"></a>
<FONT color="green">818</FONT>         *    Lookup intVal = exp(int(x))<a name="line.818"></a>
<FONT color="green">819</FONT>         *    Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 );<a name="line.819"></a>
<FONT color="green">820</FONT>         *    Compute z as the exponential of the remaining bits by a polynomial minus one<a name="line.820"></a>
<FONT color="green">821</FONT>         *    exp(x) = intVal * fracVal * (1 + z)<a name="line.821"></a>
<FONT color="green">822</FONT>         *<a name="line.822"></a>
<FONT color="green">823</FONT>         * Accuracy:<a name="line.823"></a>
<FONT color="green">824</FONT>         *    Calculation is done with 63 bits of precision, so result should be correctly<a name="line.824"></a>
<FONT color="green">825</FONT>         *    rounded for 99.9% of input values, with less than 1 ULP error otherwise.<a name="line.825"></a>
<FONT color="green">826</FONT>         *<a name="line.826"></a>
<FONT color="green">827</FONT>         * @param x   a double<a name="line.827"></a>
<FONT color="green">828</FONT>         * @return double e&lt;sup&gt;x&lt;/sup&gt;<a name="line.828"></a>
<FONT color="green">829</FONT>         */<a name="line.829"></a>
<FONT color="green">830</FONT>        public static double exp(double x) {<a name="line.830"></a>
<FONT color="green">831</FONT>            return exp(x, 0.0, null);<a name="line.831"></a>
<FONT color="green">832</FONT>        }<a name="line.832"></a>
<FONT color="green">833</FONT>    <a name="line.833"></a>
<FONT color="green">834</FONT>        /**<a name="line.834"></a>
<FONT color="green">835</FONT>         * Internal helper method for exponential function.<a name="line.835"></a>
<FONT color="green">836</FONT>         * @param x original argument of the exponential function<a name="line.836"></a>
<FONT color="green">837</FONT>         * @param extra extra bits of precision on input (To Be Confirmed)<a name="line.837"></a>
<FONT color="green">838</FONT>         * @param hiPrec extra bits of precision on output (To Be Confirmed)<a name="line.838"></a>
<FONT color="green">839</FONT>         * @return exp(x)<a name="line.839"></a>
<FONT color="green">840</FONT>         */<a name="line.840"></a>
<FONT color="green">841</FONT>        private static double exp(double x, double extra, double[] hiPrec) {<a name="line.841"></a>
<FONT color="green">842</FONT>            double intPartA;<a name="line.842"></a>
<FONT color="green">843</FONT>            double intPartB;<a name="line.843"></a>
<FONT color="green">844</FONT>            int intVal;<a name="line.844"></a>
<FONT color="green">845</FONT>    <a name="line.845"></a>
<FONT color="green">846</FONT>            /* Lookup exp(floor(x)).<a name="line.846"></a>
<FONT color="green">847</FONT>             * intPartA will have the upper 22 bits, intPartB will have the lower<a name="line.847"></a>
<FONT color="green">848</FONT>             * 52 bits.<a name="line.848"></a>
<FONT color="green">849</FONT>             */<a name="line.849"></a>
<FONT color="green">850</FONT>            if (x &lt; 0.0) {<a name="line.850"></a>
<FONT color="green">851</FONT>                intVal = (int) -x;<a name="line.851"></a>
<FONT color="green">852</FONT>    <a name="line.852"></a>
<FONT color="green">853</FONT>                if (intVal &gt; 746) {<a name="line.853"></a>
<FONT color="green">854</FONT>                    if (hiPrec != null) {<a name="line.854"></a>
<FONT color="green">855</FONT>                        hiPrec[0] = 0.0;<a name="line.855"></a>
<FONT color="green">856</FONT>                        hiPrec[1] = 0.0;<a name="line.856"></a>
<FONT color="green">857</FONT>                    }<a name="line.857"></a>
<FONT color="green">858</FONT>                    return 0.0;<a name="line.858"></a>
<FONT color="green">859</FONT>                }<a name="line.859"></a>
<FONT color="green">860</FONT>    <a name="line.860"></a>
<FONT color="green">861</FONT>                if (intVal &gt; 709) {<a name="line.861"></a>
<FONT color="green">862</FONT>                    /* This will produce a subnormal output */<a name="line.862"></a>
<FONT color="green">863</FONT>                    final double result = exp(x+40.19140625, extra, hiPrec) / 285040095144011776.0;<a name="line.863"></a>
<FONT color="green">864</FONT>                    if (hiPrec != null) {<a name="line.864"></a>
<FONT color="green">865</FONT>                        hiPrec[0] /= 285040095144011776.0;<a name="line.865"></a>
<FONT color="green">866</FONT>                        hiPrec[1] /= 285040095144011776.0;<a name="line.866"></a>
<FONT color="green">867</FONT>                    }<a name="line.867"></a>
<FONT color="green">868</FONT>                    return result;<a name="line.868"></a>
<FONT color="green">869</FONT>                }<a name="line.869"></a>
<FONT color="green">870</FONT>    <a name="line.870"></a>
<FONT color="green">871</FONT>                if (intVal == 709) {<a name="line.871"></a>
<FONT color="green">872</FONT>                    /* exp(1.494140625) is nearly a machine number... */<a name="line.872"></a>
<FONT color="green">873</FONT>                    final double result = exp(x+1.494140625, extra, hiPrec) / 4.455505956692756620;<a name="line.873"></a>
<FONT color="green">874</FONT>                    if (hiPrec != null) {<a name="line.874"></a>
<FONT color="green">875</FONT>                        hiPrec[0] /= 4.455505956692756620;<a name="line.875"></a>
<FONT color="green">876</FONT>                        hiPrec[1] /= 4.455505956692756620;<a name="line.876"></a>
<FONT color="green">877</FONT>                    }<a name="line.877"></a>
<FONT color="green">878</FONT>                    return result;<a name="line.878"></a>
<FONT color="green">879</FONT>                }<a name="line.879"></a>
<FONT color="green">880</FONT>    <a name="line.880"></a>
<FONT color="green">881</FONT>                intVal++;<a name="line.881"></a>
<FONT color="green">882</FONT>    <a name="line.882"></a>
<FONT color="green">883</FONT>                intPartA = ExpIntTable.EXP_INT_TABLE_A[EXP_INT_TABLE_MAX_INDEX-intVal];<a name="line.883"></a>
<FONT color="green">884</FONT>                intPartB = ExpIntTable.EXP_INT_TABLE_B[EXP_INT_TABLE_MAX_INDEX-intVal];<a name="line.884"></a>
<FONT color="green">885</FONT>    <a name="line.885"></a>
<FONT color="green">886</FONT>                intVal = -intVal;<a name="line.886"></a>
<FONT color="green">887</FONT>            } else {<a name="line.887"></a>
<FONT color="green">888</FONT>                intVal = (int) x;<a name="line.888"></a>
<FONT color="green">889</FONT>    <a name="line.889"></a>
<FONT color="green">890</FONT>                if (intVal &gt; 709) {<a name="line.890"></a>
<FONT color="green">891</FONT>                    if (hiPrec != null) {<a name="line.891"></a>
<FONT color="green">892</FONT>                        hiPrec[0] = Double.POSITIVE_INFINITY;<a name="line.892"></a>
<FONT color="green">893</FONT>                        hiPrec[1] = 0.0;<a name="line.893"></a>
<FONT color="green">894</FONT>                    }<a name="line.894"></a>
<FONT color="green">895</FONT>                    return Double.POSITIVE_INFINITY;<a name="line.895"></a>
<FONT color="green">896</FONT>                }<a name="line.896"></a>
<FONT color="green">897</FONT>    <a name="line.897"></a>
<FONT color="green">898</FONT>                intPartA = ExpIntTable.EXP_INT_TABLE_A[EXP_INT_TABLE_MAX_INDEX+intVal];<a name="line.898"></a>
<FONT color="green">899</FONT>                intPartB = ExpIntTable.EXP_INT_TABLE_B[EXP_INT_TABLE_MAX_INDEX+intVal];<a name="line.899"></a>
<FONT color="green">900</FONT>            }<a name="line.900"></a>
<FONT color="green">901</FONT>    <a name="line.901"></a>
<FONT color="green">902</FONT>            /* Get the fractional part of x, find the greatest multiple of 2^-10 less than<a name="line.902"></a>
<FONT color="green">903</FONT>             * x and look up the exp function of it.<a name="line.903"></a>
<FONT color="green">904</FONT>             * fracPartA will have the upper 22 bits, fracPartB the lower 52 bits.<a name="line.904"></a>
<FONT color="green">905</FONT>             */<a name="line.905"></a>
<FONT color="green">906</FONT>            final int intFrac = (int) ((x - intVal) * 1024.0);<a name="line.906"></a>
<FONT color="green">907</FONT>            final double fracPartA = ExpFracTable.EXP_FRAC_TABLE_A[intFrac];<a name="line.907"></a>
<FONT color="green">908</FONT>            final double fracPartB = ExpFracTable.EXP_FRAC_TABLE_B[intFrac];<a name="line.908"></a>
<FONT color="green">909</FONT>    <a name="line.909"></a>
<FONT color="green">910</FONT>            /* epsilon is the difference in x from the nearest multiple of 2^-10.  It<a name="line.910"></a>
<FONT color="green">911</FONT>             * has a value in the range 0 &lt;= epsilon &lt; 2^-10.<a name="line.911"></a>
<FONT color="green">912</FONT>             * Do the subtraction from x as the last step to avoid possible loss of percison.<a name="line.912"></a>
<FONT color="green">913</FONT>             */<a name="line.913"></a>
<FONT color="green">914</FONT>            final double epsilon = x - (intVal + intFrac / 1024.0);<a name="line.914"></a>
<FONT color="green">915</FONT>    <a name="line.915"></a>
<FONT color="green">916</FONT>            /* Compute z = exp(epsilon) - 1.0 via a minimax polynomial.  z has<a name="line.916"></a>
<FONT color="green">917</FONT>           full double precision (52 bits).  Since z &lt; 2^-10, we will have<a name="line.917"></a>
<FONT color="green">918</FONT>           62 bits of precision when combined with the contant 1.  This will be<a name="line.918"></a>
<FONT color="green">919</FONT>           used in the last addition below to get proper rounding. */<a name="line.919"></a>
<FONT color="green">920</FONT>    <a name="line.920"></a>
<FONT color="green">921</FONT>            /* Remez generated polynomial.  Converges on the interval [0, 2^-10], error<a name="line.921"></a>
<FONT color="green">922</FONT>           is less than 0.5 ULP */<a name="line.922"></a>
<FONT color="green">923</FONT>            double z = 0.04168701738764507;<a name="line.923"></a>
<FONT color="green">924</FONT>            z = z * epsilon + 0.1666666505023083;<a name="line.924"></a>
<FONT color="green">925</FONT>            z = z * epsilon + 0.5000000000042687;<a name="line.925"></a>
<FONT color="green">926</FONT>            z = z * epsilon + 1.0;<a name="line.926"></a>
<FONT color="green">927</FONT>            z = z * epsilon + -3.940510424527919E-20;<a name="line.927"></a>
<FONT color="green">928</FONT>    <a name="line.928"></a>
<FONT color="green">929</FONT>            /* Compute (intPartA+intPartB) * (fracPartA+fracPartB) by binomial<a name="line.929"></a>
<FONT color="green">930</FONT>           expansion.<a name="line.930"></a>
<FONT color="green">931</FONT>           tempA is exact since intPartA and intPartB only have 22 bits each.<a name="line.931"></a>
<FONT color="green">932</FONT>           tempB will have 52 bits of precision.<a name="line.932"></a>
<FONT color="green">933</FONT>             */<a name="line.933"></a>
<FONT color="green">934</FONT>            double tempA = intPartA * fracPartA;<a name="line.934"></a>
<FONT color="green">935</FONT>            double tempB = intPartA * fracPartB + intPartB * fracPartA + intPartB * fracPartB;<a name="line.935"></a>
<FONT color="green">936</FONT>    <a name="line.936"></a>
<FONT color="green">937</FONT>            /* Compute the result.  (1+z)(tempA+tempB).  Order of operations is<a name="line.937"></a>
<FONT color="green">938</FONT>           important.  For accuracy add by increasing size.  tempA is exact and<a name="line.938"></a>
<FONT color="green">939</FONT>           much larger than the others.  If there are extra bits specified from the<a name="line.939"></a>
<FONT color="green">940</FONT>           pow() function, use them. */<a name="line.940"></a>
<FONT color="green">941</FONT>            final double tempC = tempB + tempA;<a name="line.941"></a>
<FONT color="green">942</FONT>            final double result;<a name="line.942"></a>
<FONT color="green">943</FONT>            if (extra != 0.0) {<a name="line.943"></a>
<FONT color="green">944</FONT>                result = tempC*extra*z + tempC*extra + tempC*z + tempB + tempA;<a name="line.944"></a>
<FONT color="green">945</FONT>            } else {<a name="line.945"></a>
<FONT color="green">946</FONT>                result = tempC*z + tempB + tempA;<a name="line.946"></a>
<FONT color="green">947</FONT>            }<a name="line.947"></a>
<FONT color="green">948</FONT>    <a name="line.948"></a>
<FONT color="green">949</FONT>            if (hiPrec != null) {<a name="line.949"></a>
<FONT color="green">950</FONT>                // If requesting high precision<a name="line.950"></a>
<FONT color="green">951</FONT>                hiPrec[0] = tempA;<a name="line.951"></a>
<FONT color="green">952</FONT>                hiPrec[1] = tempC*extra*z + tempC*extra + tempC*z + tempB;<a name="line.952"></a>
<FONT color="green">953</FONT>            }<a name="line.953"></a>
<FONT color="green">954</FONT>    <a name="line.954"></a>
<FONT color="green">955</FONT>            return result;<a name="line.955"></a>
<FONT color="green">956</FONT>        }<a name="line.956"></a>
<FONT color="green">957</FONT>    <a name="line.957"></a>
<FONT color="green">958</FONT>        /** Compute exp(x) - 1<a name="line.958"></a>
<FONT color="green">959</FONT>         * @param x number to compute shifted exponential<a name="line.959"></a>
<FONT color="green">960</FONT>         * @return exp(x) - 1<a name="line.960"></a>
<FONT color="green">961</FONT>         */<a name="line.961"></a>
<FONT color="green">962</FONT>        public static double expm1(double x) {<a name="line.962"></a>
<FONT color="green">963</FONT>          return expm1(x, null);<a name="line.963"></a>
<FONT color="green">964</FONT>        }<a name="line.964"></a>
<FONT color="green">965</FONT>    <a name="line.965"></a>
<FONT color="green">966</FONT>        /** Internal helper method for expm1<a name="line.966"></a>
<FONT color="green">967</FONT>         * @param x number to compute shifted exponential<a name="line.967"></a>
<FONT color="green">968</FONT>         * @param hiPrecOut receive high precision result for -1.0 &lt; x &lt; 1.0<a name="line.968"></a>
<FONT color="green">969</FONT>         * @return exp(x) - 1<a name="line.969"></a>
<FONT color="green">970</FONT>         */<a name="line.970"></a>
<FONT color="green">971</FONT>        private static double expm1(double x, double hiPrecOut[]) {<a name="line.971"></a>
<FONT color="green">972</FONT>            if (x != x || x == 0.0) { // NaN or zero<a name="line.972"></a>
<FONT color="green">973</FONT>                return x;<a name="line.973"></a>
<FONT color="green">974</FONT>            }<a name="line.974"></a>
<FONT color="green">975</FONT>    <a name="line.975"></a>
<FONT color="green">976</FONT>            if (x &lt;= -1.0 || x &gt;= 1.0) {<a name="line.976"></a>
<FONT color="green">977</FONT>                // If not between +/- 1.0<a name="line.977"></a>
<FONT color="green">978</FONT>                //return exp(x) - 1.0;<a name="line.978"></a>
<FONT color="green">979</FONT>                double hiPrec[] = new double[2];<a name="line.979"></a>
<FONT color="green">980</FONT>                exp(x, 0.0, hiPrec);<a name="line.980"></a>
<FONT color="green">981</FONT>                if (x &gt; 0.0) {<a name="line.981"></a>
<FONT color="green">982</FONT>                    return -1.0 + hiPrec[0] + hiPrec[1];<a name="line.982"></a>
<FONT color="green">983</FONT>                } else {<a name="line.983"></a>
<FONT color="green">984</FONT>                    final double ra = -1.0 + hiPrec[0];<a name="line.984"></a>
<FONT color="green">985</FONT>                    double rb = -(ra + 1.0 - hiPrec[0]);<a name="line.985"></a>
<FONT color="green">986</FONT>                    rb += hiPrec[1];<a name="line.986"></a>
<FONT color="green">987</FONT>                    return ra + rb;<a name="line.987"></a>
<FONT color="green">988</FONT>                }<a name="line.988"></a>
<FONT color="green">989</FONT>            }<a name="line.989"></a>
<FONT color="green">990</FONT>    <a name="line.990"></a>
<FONT color="green">991</FONT>            double baseA;<a name="line.991"></a>
<FONT color="green">992</FONT>            double baseB;<a name="line.992"></a>
<FONT color="green">993</FONT>            double epsilon;<a name="line.993"></a>
<FONT color="green">994</FONT>            boolean negative = false;<a name="line.994"></a>
<FONT color="green">995</FONT>    <a name="line.995"></a>
<FONT color="green">996</FONT>            if (x &lt; 0.0) {<a name="line.996"></a>
<FONT color="green">997</FONT>                x = -x;<a name="line.997"></a>
<FONT color="green">998</FONT>                negative = true;<a name="line.998"></a>
<FONT color="green">999</FONT>            }<a name="line.999"></a>
<FONT color="green">1000</FONT>    <a name="line.1000"></a>
<FONT color="green">1001</FONT>            {<a name="line.1001"></a>
<FONT color="green">1002</FONT>                int intFrac = (int) (x * 1024.0);<a name="line.1002"></a>
<FONT color="green">1003</FONT>                double tempA = ExpFracTable.EXP_FRAC_TABLE_A[intFrac] - 1.0;<a name="line.1003"></a>
<FONT color="green">1004</FONT>                double tempB = ExpFracTable.EXP_FRAC_TABLE_B[intFrac];<a name="line.1004"></a>
<FONT color="green">1005</FONT>    <a name="line.1005"></a>
<FONT color="green">1006</FONT>                double temp = tempA + tempB;<a name="line.1006"></a>
<FONT color="green">1007</FONT>                tempB = -(temp - tempA - tempB);<a name="line.1007"></a>
<FONT color="green">1008</FONT>                tempA = temp;<a name="line.1008"></a>
<FONT color="green">1009</FONT>    <a name="line.1009"></a>
<FONT color="green">1010</FONT>                temp = tempA * HEX_40000000;<a name="line.1010"></a>
<FONT color="green">1011</FONT>                baseA = tempA + temp - temp;<a name="line.1011"></a>
<FONT color="green">1012</FONT>                baseB = tempB + (tempA - baseA);<a name="line.1012"></a>
<FONT color="green">1013</FONT>    <a name="line.1013"></a>
<FONT color="green">1014</FONT>                epsilon = x - intFrac/1024.0;<a name="line.1014"></a>
<FONT color="green">1015</FONT>            }<a name="line.1015"></a>
<FONT color="green">1016</FONT>    <a name="line.1016"></a>
<FONT color="green">1017</FONT>    <a name="line.1017"></a>
<FONT color="green">1018</FONT>            /* Compute expm1(epsilon) */<a name="line.1018"></a>
<FONT color="green">1019</FONT>            double zb = 0.008336750013465571;<a name="line.1019"></a>
<FONT color="green">1020</FONT>            zb = zb * epsilon + 0.041666663879186654;<a name="line.1020"></a>
<FONT color="green">1021</FONT>            zb = zb * epsilon + 0.16666666666745392;<a name="line.1021"></a>
<FONT color="green">1022</FONT>            zb = zb * epsilon + 0.49999999999999994;<a name="line.1022"></a>
<FONT color="green">1023</FONT>            zb = zb * epsilon;<a name="line.1023"></a>
<FONT color="green">1024</FONT>            zb = zb * epsilon;<a name="line.1024"></a>
<FONT color="green">1025</FONT>    <a name="line.1025"></a>
<FONT color="green">1026</FONT>            double za = epsilon;<a name="line.1026"></a>
<FONT color="green">1027</FONT>            double temp = za + zb;<a name="line.1027"></a>
<FONT color="green">1028</FONT>            zb = -(temp - za - zb);<a name="line.1028"></a>
<FONT color="green">1029</FONT>            za = temp;<a name="line.1029"></a>
<FONT color="green">1030</FONT>    <a name="line.1030"></a>
<FONT color="green">1031</FONT>            temp = za * HEX_40000000;<a name="line.1031"></a>
<FONT color="green">1032</FONT>            temp = za + temp - temp;<a name="line.1032"></a>
<FONT color="green">1033</FONT>            zb += za - temp;<a name="line.1033"></a>
<FONT color="green">1034</FONT>            za = temp;<a name="line.1034"></a>
<FONT color="green">1035</FONT>    <a name="line.1035"></a>
<FONT color="green">1036</FONT>            /* Combine the parts.   expm1(a+b) = expm1(a) + expm1(b) + expm1(a)*expm1(b) */<a name="line.1036"></a>
<FONT color="green">1037</FONT>            double ya = za * baseA;<a name="line.1037"></a>
<FONT color="green">1038</FONT>            //double yb = za*baseB + zb*baseA + zb*baseB;<a name="line.1038"></a>
<FONT color="green">1039</FONT>            temp = ya + za * baseB;<a name="line.1039"></a>
<FONT color="green">1040</FONT>            double yb = -(temp - ya - za * baseB);<a name="line.1040"></a>
<FONT color="green">1041</FONT>            ya = temp;<a name="line.1041"></a>
<FONT color="green">1042</FONT>    <a name="line.1042"></a>
<FONT color="green">1043</FONT>            temp = ya + zb * baseA;<a name="line.1043"></a>
<FONT color="green">1044</FONT>            yb += -(temp - ya - zb * baseA);<a name="line.1044"></a>
<FONT color="green">1045</FONT>            ya = temp;<a name="line.1045"></a>
<FONT color="green">1046</FONT>    <a name="line.1046"></a>
<FONT color="green">1047</FONT>            temp = ya + zb * baseB;<a name="line.1047"></a>
<FONT color="green">1048</FONT>            yb += -(temp - ya - zb*baseB);<a name="line.1048"></a>
<FONT color="green">1049</FONT>            ya = temp;<a name="line.1049"></a>
<FONT color="green">1050</FONT>    <a name="line.1050"></a>
<FONT color="green">1051</FONT>            //ya = ya + za + baseA;<a name="line.1051"></a>
<FONT color="green">1052</FONT>            //yb = yb + zb + baseB;<a name="line.1052"></a>
<FONT color="green">1053</FONT>            temp = ya + baseA;<a name="line.1053"></a>
<FONT color="green">1054</FONT>            yb += -(temp - baseA - ya);<a name="line.1054"></a>
<FONT color="green">1055</FONT>            ya = temp;<a name="line.1055"></a>
<FONT color="green">1056</FONT>    <a name="line.1056"></a>
<FONT color="green">1057</FONT>            temp = ya + za;<a name="line.1057"></a>
<FONT color="green">1058</FONT>            //yb += (ya &gt; za) ? -(temp - ya - za) : -(temp - za - ya);<a name="line.1058"></a>
<FONT color="green">1059</FONT>            yb += -(temp - ya - za);<a name="line.1059"></a>
<FONT color="green">1060</FONT>            ya = temp;<a name="line.1060"></a>
<FONT color="green">1061</FONT>    <a name="line.1061"></a>
<FONT color="green">1062</FONT>            temp = ya + baseB;<a name="line.1062"></a>
<FONT color="green">1063</FONT>            //yb += (ya &gt; baseB) ? -(temp - ya - baseB) : -(temp - baseB - ya);<a name="line.1063"></a>
<FONT color="green">1064</FONT>            yb += -(temp - ya - baseB);<a name="line.1064"></a>
<FONT color="green">1065</FONT>            ya = temp;<a name="line.1065"></a>
<FONT color="green">1066</FONT>    <a name="line.1066"></a>
<FONT color="green">1067</FONT>            temp = ya + zb;<a name="line.1067"></a>
<FONT color="green">1068</FONT>            //yb += (ya &gt; zb) ? -(temp - ya - zb) : -(temp - zb - ya);<a name="line.1068"></a>
<FONT color="green">1069</FONT>            yb += -(temp - ya - zb);<a name="line.1069"></a>
<FONT color="green">1070</FONT>            ya = temp;<a name="line.1070"></a>
<FONT color="green">1071</FONT>    <a name="line.1071"></a>
<FONT color="green">1072</FONT>            if (negative) {<a name="line.1072"></a>
<FONT color="green">1073</FONT>                /* Compute expm1(-x) = -expm1(x) / (expm1(x) + 1) */<a name="line.1073"></a>
<FONT color="green">1074</FONT>                double denom = 1.0 + ya;<a name="line.1074"></a>
<FONT color="green">1075</FONT>                double denomr = 1.0 / denom;<a name="line.1075"></a>
<FONT color="green">1076</FONT>                double denomb = -(denom - 1.0 - ya) + yb;<a name="line.1076"></a>
<FONT color="green">1077</FONT>                double ratio = ya * denomr;<a name="line.1077"></a>
<FONT color="green">1078</FONT>                temp = ratio * HEX_40000000;<a name="line.1078"></a>
<FONT color="green">1079</FONT>                final double ra = ratio + temp - temp;<a name="line.1079"></a>
<FONT color="green">1080</FONT>                double rb = ratio - ra;<a name="line.1080"></a>
<FONT color="green">1081</FONT>    <a name="line.1081"></a>
<FONT color="green">1082</FONT>                temp = denom * HEX_40000000;<a name="line.1082"></a>
<FONT color="green">1083</FONT>                za = denom + temp - temp;<a name="line.1083"></a>
<FONT color="green">1084</FONT>                zb = denom - za;<a name="line.1084"></a>
<FONT color="green">1085</FONT>    <a name="line.1085"></a>
<FONT color="green">1086</FONT>                rb += (ya - za * ra - za * rb - zb * ra - zb * rb) * denomr;<a name="line.1086"></a>
<FONT color="green">1087</FONT>    <a name="line.1087"></a>
<FONT color="green">1088</FONT>                // f(x) = x/1+x<a name="line.1088"></a>
<FONT color="green">1089</FONT>                // Compute f'(x)<a name="line.1089"></a>
<FONT color="green">1090</FONT>                // Product rule:  d(uv) = du*v + u*dv<a name="line.1090"></a>
<FONT color="green">1091</FONT>                // Chain rule:  d(f(g(x)) = f'(g(x))*f(g'(x))<a name="line.1091"></a>
<FONT color="green">1092</FONT>                // d(1/x) = -1/(x*x)<a name="line.1092"></a>
<FONT color="green">1093</FONT>                // d(1/1+x) = -1/( (1+x)^2) *  1 =  -1/((1+x)*(1+x))<a name="line.1093"></a>
<FONT color="green">1094</FONT>                // d(x/1+x) = -x/((1+x)(1+x)) + 1/1+x = 1 / ((1+x)(1+x))<a name="line.1094"></a>
<FONT color="green">1095</FONT>    <a name="line.1095"></a>
<FONT color="green">1096</FONT>                // Adjust for yb<a name="line.1096"></a>
<FONT color="green">1097</FONT>                rb += yb * denomr;                      // numerator<a name="line.1097"></a>
<FONT color="green">1098</FONT>                rb += -ya * denomb * denomr * denomr;   // denominator<a name="line.1098"></a>
<FONT color="green">1099</FONT>    <a name="line.1099"></a>
<FONT color="green">1100</FONT>                // negate<a name="line.1100"></a>
<FONT color="green">1101</FONT>                ya = -ra;<a name="line.1101"></a>
<FONT color="green">1102</FONT>                yb = -rb;<a name="line.1102"></a>
<FONT color="green">1103</FONT>            }<a name="line.1103"></a>
<FONT color="green">1104</FONT>    <a name="line.1104"></a>
<FONT color="green">1105</FONT>            if (hiPrecOut != null) {<a name="line.1105"></a>
<FONT color="green">1106</FONT>                hiPrecOut[0] = ya;<a name="line.1106"></a>
<FONT color="green">1107</FONT>                hiPrecOut[1] = yb;<a name="line.1107"></a>
<FONT color="green">1108</FONT>            }<a name="line.1108"></a>
<FONT color="green">1109</FONT>    <a name="line.1109"></a>
<FONT color="green">1110</FONT>            return ya + yb;<a name="line.1110"></a>
<FONT color="green">1111</FONT>        }<a name="line.1111"></a>
<FONT color="green">1112</FONT>    <a name="line.1112"></a>
<FONT color="green">1113</FONT>        /**<a name="line.1113"></a>
<FONT color="green">1114</FONT>         * Natural logarithm.<a name="line.1114"></a>
<FONT color="green">1115</FONT>         *<a name="line.1115"></a>
<FONT color="green">1116</FONT>         * @param x   a double<a name="line.1116"></a>
<FONT color="green">1117</FONT>         * @return log(x)<a name="line.1117"></a>
<FONT color="green">1118</FONT>         */<a name="line.1118"></a>
<FONT color="green">1119</FONT>        public static double log(final double x) {<a name="line.1119"></a>
<FONT color="green">1120</FONT>            return log(x, null);<a name="line.1120"></a>
<FONT color="green">1121</FONT>        }<a name="line.1121"></a>
<FONT color="green">1122</FONT>    <a name="line.1122"></a>
<FONT color="green">1123</FONT>        /**<a name="line.1123"></a>
<FONT color="green">1124</FONT>         * Internal helper method for natural logarithm function.<a name="line.1124"></a>
<FONT color="green">1125</FONT>         * @param x original argument of the natural logarithm function<a name="line.1125"></a>
<FONT color="green">1126</FONT>         * @param hiPrec extra bits of precision on output (To Be Confirmed)<a name="line.1126"></a>
<FONT color="green">1127</FONT>         * @return log(x)<a name="line.1127"></a>
<FONT color="green">1128</FONT>         */<a name="line.1128"></a>
<FONT color="green">1129</FONT>        private static double log(final double x, final double[] hiPrec) {<a name="line.1129"></a>
<FONT color="green">1130</FONT>            if (x==0) { // Handle special case of +0/-0<a name="line.1130"></a>
<FONT color="green">1131</FONT>                return Double.NEGATIVE_INFINITY;<a name="line.1131"></a>
<FONT color="green">1132</FONT>            }<a name="line.1132"></a>
<FONT color="green">1133</FONT>            long bits = Double.doubleToLongBits(x);<a name="line.1133"></a>
<FONT color="green">1134</FONT>    <a name="line.1134"></a>
<FONT color="green">1135</FONT>            /* Handle special cases of negative input, and NaN */<a name="line.1135"></a>
<FONT color="green">1136</FONT>            if ((bits &amp; 0x8000000000000000L) != 0 || x != x) {<a name="line.1136"></a>
<FONT color="green">1137</FONT>                if (x != 0.0) {<a name="line.1137"></a>
<FONT color="green">1138</FONT>                    if (hiPrec != null) {<a name="line.1138"></a>
<FONT color="green">1139</FONT>                        hiPrec[0] = Double.NaN;<a name="line.1139"></a>
<FONT color="green">1140</FONT>                    }<a name="line.1140"></a>
<FONT color="green">1141</FONT>    <a name="line.1141"></a>
<FONT color="green">1142</FONT>                    return Double.NaN;<a name="line.1142"></a>
<FONT color="green">1143</FONT>                }<a name="line.1143"></a>
<FONT color="green">1144</FONT>            }<a name="line.1144"></a>
<FONT color="green">1145</FONT>    <a name="line.1145"></a>
<FONT color="green">1146</FONT>            /* Handle special cases of Positive infinity. */<a name="line.1146"></a>
<FONT color="green">1147</FONT>            if (x == Double.POSITIVE_INFINITY) {<a name="line.1147"></a>
<FONT color="green">1148</FONT>                if (hiPrec != null) {<a name="line.1148"></a>
<FONT color="green">1149</FONT>                    hiPrec[0] = Double.POSITIVE_INFINITY;<a name="line.1149"></a>
<FONT color="green">1150</FONT>                }<a name="line.1150"></a>
<FONT color="green">1151</FONT>    <a name="line.1151"></a>
<FONT color="green">1152</FONT>                return Double.POSITIVE_INFINITY;<a name="line.1152"></a>
<FONT color="green">1153</FONT>            }<a name="line.1153"></a>
<FONT color="green">1154</FONT>    <a name="line.1154"></a>
<FONT color="green">1155</FONT>            /* Extract the exponent */<a name="line.1155"></a>
<FONT color="green">1156</FONT>            int exp = (int)(bits &gt;&gt; 52)-1023;<a name="line.1156"></a>
<FONT color="green">1157</FONT>    <a name="line.1157"></a>
<FONT color="green">1158</FONT>            if ((bits &amp; 0x7ff0000000000000L) == 0) {<a name="line.1158"></a>
<FONT color="green">1159</FONT>                // Subnormal!<a name="line.1159"></a>
<FONT color="green">1160</FONT>                if (x == 0) {<a name="line.1160"></a>
<FONT color="green">1161</FONT>                    // Zero<a name="line.1161"></a>
<FONT color="green">1162</FONT>                    if (hiPrec != null) {<a name="line.1162"></a>
<FONT color="green">1163</FONT>                        hiPrec[0] = Double.NEGATIVE_INFINITY;<a name="line.1163"></a>
<FONT color="green">1164</FONT>                    }<a name="line.1164"></a>
<FONT color="green">1165</FONT>    <a name="line.1165"></a>
<FONT color="green">1166</FONT>                    return Double.NEGATIVE_INFINITY;<a name="line.1166"></a>
<FONT color="green">1167</FONT>                }<a name="line.1167"></a>
<FONT color="green">1168</FONT>    <a name="line.1168"></a>
<FONT color="green">1169</FONT>                /* Normalize the subnormal number. */<a name="line.1169"></a>
<FONT color="green">1170</FONT>                bits &lt;&lt;= 1;<a name="line.1170"></a>
<FONT color="green">1171</FONT>                while ( (bits &amp; 0x0010000000000000L) == 0) {<a name="line.1171"></a>
<FONT color="green">1172</FONT>                    --exp;<a name="line.1172"></a>
<FONT color="green">1173</FONT>                    bits &lt;&lt;= 1;<a name="line.1173"></a>
<FONT color="green">1174</FONT>                }<a name="line.1174"></a>
<FONT color="green">1175</FONT>            }<a name="line.1175"></a>
<FONT color="green">1176</FONT>    <a name="line.1176"></a>
<FONT color="green">1177</FONT>    <a name="line.1177"></a>
<FONT color="green">1178</FONT>            if (exp == -1 || exp == 0) {<a name="line.1178"></a>
<FONT color="green">1179</FONT>                if (x &lt; 1.01 &amp;&amp; x &gt; 0.99 &amp;&amp; hiPrec == null) {<a name="line.1179"></a>
<FONT color="green">1180</FONT>                    /* The normal method doesn't work well in the range [0.99, 1.01], so call do a straight<a name="line.1180"></a>
<FONT color="green">1181</FONT>               polynomial expansion in higer precision. */<a name="line.1181"></a>
<FONT color="green">1182</FONT>    <a name="line.1182"></a>
<FONT color="green">1183</FONT>                   /* Compute x - 1.0 and split it */<a name="line.1183"></a>
<FONT color="green">1184</FONT>                    double xa = x - 1.0;<a name="line.1184"></a>
<FONT color="green">1185</FONT>                    double xb = xa - x + 1.0;<a name="line.1185"></a>
<FONT color="green">1186</FONT>                    double tmp = xa * HEX_40000000;<a name="line.1186"></a>
<FONT color="green">1187</FONT>                    double aa = xa + tmp - tmp;<a name="line.1187"></a>
<FONT color="green">1188</FONT>                    double ab = xa - aa;<a name="line.1188"></a>
<FONT color="green">1189</FONT>                    xa = aa;<a name="line.1189"></a>
<FONT color="green">1190</FONT>                    xb = ab;<a name="line.1190"></a>
<FONT color="green">1191</FONT>    <a name="line.1191"></a>
<FONT color="green">1192</FONT>                    final double[] lnCoef_last = LN_QUICK_COEF[LN_QUICK_COEF.length - 1];<a name="line.1192"></a>
<FONT color="green">1193</FONT>                    double ya = lnCoef_last[0];<a name="line.1193"></a>
<FONT color="green">1194</FONT>                    double yb = lnCoef_last[1];<a name="line.1194"></a>
<FONT color="green">1195</FONT>    <a name="line.1195"></a>
<FONT color="green">1196</FONT>                    for (int i = LN_QUICK_COEF.length - 2; i &gt;= 0; i--) {<a name="line.1196"></a>
<FONT color="green">1197</FONT>                        /* Multiply a = y * x */<a name="line.1197"></a>
<FONT color="green">1198</FONT>                        aa = ya * xa;<a name="line.1198"></a>
<FONT color="green">1199</FONT>                        ab = ya * xb + yb * xa + yb * xb;<a name="line.1199"></a>
<FONT color="green">1200</FONT>                        /* split, so now y = a */<a name="line.1200"></a>
<FONT color="green">1201</FONT>                        tmp = aa * HEX_40000000;<a name="line.1201"></a>
<FONT color="green">1202</FONT>                        ya = aa + tmp - tmp;<a name="line.1202"></a>
<FONT color="green">1203</FONT>                        yb = aa - ya + ab;<a name="line.1203"></a>
<FONT color="green">1204</FONT>    <a name="line.1204"></a>
<FONT color="green">1205</FONT>                        /* Add  a = y + lnQuickCoef */<a name="line.1205"></a>
<FONT color="green">1206</FONT>                        final double[] lnCoef_i = LN_QUICK_COEF[i];<a name="line.1206"></a>
<FONT color="green">1207</FONT>                        aa = ya + lnCoef_i[0];<a name="line.1207"></a>
<FONT color="green">1208</FONT>                        ab = yb + lnCoef_i[1];<a name="line.1208"></a>
<FONT color="green">1209</FONT>                        /* Split y = a */<a name="line.1209"></a>
<FONT color="green">1210</FONT>                        tmp = aa * HEX_40000000;<a name="line.1210"></a>
<FONT color="green">1211</FONT>                        ya = aa + tmp - tmp;<a name="line.1211"></a>
<FONT color="green">1212</FONT>                        yb = aa - ya + ab;<a name="line.1212"></a>
<FONT color="green">1213</FONT>                    }<a name="line.1213"></a>
<FONT color="green">1214</FONT>    <a name="line.1214"></a>
<FONT color="green">1215</FONT>                    /* Multiply a = y * x */<a name="line.1215"></a>
<FONT color="green">1216</FONT>                    aa = ya * xa;<a name="line.1216"></a>
<FONT color="green">1217</FONT>                    ab = ya * xb + yb * xa + yb * xb;<a name="line.1217"></a>
<FONT color="green">1218</FONT>                    /* split, so now y = a */<a name="line.1218"></a>
<FONT color="green">1219</FONT>                    tmp = aa * HEX_40000000;<a name="line.1219"></a>
<FONT color="green">1220</FONT>                    ya = aa + tmp - tmp;<a name="line.1220"></a>
<FONT color="green">1221</FONT>                    yb = aa - ya + ab;<a name="line.1221"></a>
<FONT color="green">1222</FONT>    <a name="line.1222"></a>
<FONT color="green">1223</FONT>                    return ya + yb;<a name="line.1223"></a>
<FONT color="green">1224</FONT>                }<a name="line.1224"></a>
<FONT color="green">1225</FONT>            }<a name="line.1225"></a>
<FONT color="green">1226</FONT>    <a name="line.1226"></a>
<FONT color="green">1227</FONT>            // lnm is a log of a number in the range of 1.0 - 2.0, so 0 &lt;= lnm &lt; ln(2)<a name="line.1227"></a>
<FONT color="green">1228</FONT>            final double[] lnm = lnMant.LN_MANT[(int)((bits &amp; 0x000ffc0000000000L) &gt;&gt; 42)];<a name="line.1228"></a>
<FONT color="green">1229</FONT>    <a name="line.1229"></a>
<FONT color="green">1230</FONT>            /*<a name="line.1230"></a>
<FONT color="green">1231</FONT>        double epsilon = x / Double.longBitsToDouble(bits &amp; 0xfffffc0000000000L);<a name="line.1231"></a>
<FONT color="green">1232</FONT>    <a name="line.1232"></a>
<FONT color="green">1233</FONT>        epsilon -= 1.0;<a name="line.1233"></a>
<FONT color="green">1234</FONT>             */<a name="line.1234"></a>
<FONT color="green">1235</FONT>    <a name="line.1235"></a>
<FONT color="green">1236</FONT>            // y is the most significant 10 bits of the mantissa<a name="line.1236"></a>
<FONT color="green">1237</FONT>            //double y = Double.longBitsToDouble(bits &amp; 0xfffffc0000000000L);<a name="line.1237"></a>
<FONT color="green">1238</FONT>            //double epsilon = (x - y) / y;<a name="line.1238"></a>
<FONT color="green">1239</FONT>            final double epsilon = (bits &amp; 0x3ffffffffffL) / (TWO_POWER_52 + (bits &amp; 0x000ffc0000000000L));<a name="line.1239"></a>
<FONT color="green">1240</FONT>    <a name="line.1240"></a>
<FONT color="green">1241</FONT>            double lnza = 0.0;<a name="line.1241"></a>
<FONT color="green">1242</FONT>            double lnzb = 0.0;<a name="line.1242"></a>
<FONT color="green">1243</FONT>    <a name="line.1243"></a>
<FONT color="green">1244</FONT>            if (hiPrec != null) {<a name="line.1244"></a>
<FONT color="green">1245</FONT>                /* split epsilon -&gt; x */<a name="line.1245"></a>
<FONT color="green">1246</FONT>                double tmp = epsilon * HEX_40000000;<a name="line.1246"></a>
<FONT color="green">1247</FONT>                double aa = epsilon + tmp - tmp;<a name="line.1247"></a>
<FONT color="green">1248</FONT>                double ab = epsilon - aa;<a name="line.1248"></a>
<FONT color="green">1249</FONT>                double xa = aa;<a name="line.1249"></a>
<FONT color="green">1250</FONT>                double xb = ab;<a name="line.1250"></a>
<FONT color="green">1251</FONT>    <a name="line.1251"></a>
<FONT color="green">1252</FONT>                /* Need a more accurate epsilon, so adjust the division. */<a name="line.1252"></a>
<FONT color="green">1253</FONT>                final double numer = bits &amp; 0x3ffffffffffL;<a name="line.1253"></a>
<FONT color="green">1254</FONT>                final double denom = TWO_POWER_52 + (bits &amp; 0x000ffc0000000000L);<a name="line.1254"></a>
<FONT color="green">1255</FONT>                aa = numer - xa*denom - xb * denom;<a name="line.1255"></a>
<FONT color="green">1256</FONT>                xb += aa / denom;<a name="line.1256"></a>
<FONT color="green">1257</FONT>    <a name="line.1257"></a>
<FONT color="green">1258</FONT>                /* Remez polynomial evaluation */<a name="line.1258"></a>
<FONT color="green">1259</FONT>                final double[] lnCoef_last = LN_HI_PREC_COEF[LN_HI_PREC_COEF.length-1];<a name="line.1259"></a>
<FONT color="green">1260</FONT>                double ya = lnCoef_last[0];<a name="line.1260"></a>
<FONT color="green">1261</FONT>                double yb = lnCoef_last[1];<a name="line.1261"></a>
<FONT color="green">1262</FONT>    <a name="line.1262"></a>
<FONT color="green">1263</FONT>                for (int i = LN_HI_PREC_COEF.length - 2; i &gt;= 0; i--) {<a name="line.1263"></a>
<FONT color="green">1264</FONT>                    /* Multiply a = y * x */<a name="line.1264"></a>
<FONT color="green">1265</FONT>                    aa = ya * xa;<a name="line.1265"></a>
<FONT color="green">1266</FONT>                    ab = ya * xb + yb * xa + yb * xb;<a name="line.1266"></a>
<FONT color="green">1267</FONT>                    /* split, so now y = a */<a name="line.1267"></a>
<FONT color="green">1268</FONT>                    tmp = aa * HEX_40000000;<a name="line.1268"></a>
<FONT color="green">1269</FONT>                    ya = aa + tmp - tmp;<a name="line.1269"></a>
<FONT color="green">1270</FONT>                    yb = aa - ya + ab;<a name="line.1270"></a>
<FONT color="green">1271</FONT>    <a name="line.1271"></a>
<FONT color="green">1272</FONT>                    /* Add  a = y + lnHiPrecCoef */<a name="line.1272"></a>
<FONT color="green">1273</FONT>                    final double[] lnCoef_i = LN_HI_PREC_COEF[i];<a name="line.1273"></a>
<FONT color="green">1274</FONT>                    aa = ya + lnCoef_i[0];<a name="line.1274"></a>
<FONT color="green">1275</FONT>                    ab = yb + lnCoef_i[1];<a name="line.1275"></a>
<FONT color="green">1276</FONT>                    /* Split y = a */<a name="line.1276"></a>
<FONT color="green">1277</FONT>                    tmp = aa * HEX_40000000;<a name="line.1277"></a>
<FONT color="green">1278</FONT>                    ya = aa + tmp - tmp;<a name="line.1278"></a>
<FONT color="green">1279</FONT>                    yb = aa - ya + ab;<a name="line.1279"></a>
<FONT color="green">1280</FONT>                }<a name="line.1280"></a>
<FONT color="green">1281</FONT>    <a name="line.1281"></a>
<FONT color="green">1282</FONT>                /* Multiply a = y * x */<a name="line.1282"></a>
<FONT color="green">1283</FONT>                aa = ya * xa;<a name="line.1283"></a>
<FONT color="green">1284</FONT>                ab = ya * xb + yb * xa + yb * xb;<a name="line.1284"></a>
<FONT color="green">1285</FONT>    <a name="line.1285"></a>
<FONT color="green">1286</FONT>                /* split, so now lnz = a */<a name="line.1286"></a>
<FONT color="green">1287</FONT>                /*<a name="line.1287"></a>
<FONT color="green">1288</FONT>          tmp = aa * 1073741824.0;<a name="line.1288"></a>
<FONT color="green">1289</FONT>          lnza = aa + tmp - tmp;<a name="line.1289"></a>
<FONT color="green">1290</FONT>          lnzb = aa - lnza + ab;<a name="line.1290"></a>
<FONT color="green">1291</FONT>                 */<a name="line.1291"></a>
<FONT color="green">1292</FONT>                lnza = aa + ab;<a name="line.1292"></a>
<FONT color="green">1293</FONT>                lnzb = -(lnza - aa - ab);<a name="line.1293"></a>
<FONT color="green">1294</FONT>            } else {<a name="line.1294"></a>
<FONT color="green">1295</FONT>                /* High precision not required.  Eval Remez polynomial<a name="line.1295"></a>
<FONT color="green">1296</FONT>             using standard double precision */<a name="line.1296"></a>
<FONT color="green">1297</FONT>                lnza = -0.16624882440418567;<a name="line.1297"></a>
<FONT color="green">1298</FONT>                lnza = lnza * epsilon + 0.19999954120254515;<a name="line.1298"></a>
<FONT color="green">1299</FONT>                lnza = lnza * epsilon + -0.2499999997677497;<a name="line.1299"></a>
<FONT color="green">1300</FONT>                lnza = lnza * epsilon + 0.3333333333332802;<a name="line.1300"></a>
<FONT color="green">1301</FONT>                lnza = lnza * epsilon + -0.5;<a name="line.1301"></a>
<FONT color="green">1302</FONT>                lnza = lnza * epsilon + 1.0;<a name="line.1302"></a>
<FONT color="green">1303</FONT>                lnza = lnza * epsilon;<a name="line.1303"></a>
<FONT color="green">1304</FONT>            }<a name="line.1304"></a>
<FONT color="green">1305</FONT>    <a name="line.1305"></a>
<FONT color="green">1306</FONT>            /* Relative sizes:<a name="line.1306"></a>
<FONT color="green">1307</FONT>             * lnzb     [0, 2.33E-10]<a name="line.1307"></a>
<FONT color="green">1308</FONT>             * lnm[1]   [0, 1.17E-7]<a name="line.1308"></a>
<FONT color="green">1309</FONT>             * ln2B*exp [0, 1.12E-4]<a name="line.1309"></a>
<FONT color="green">1310</FONT>             * lnza      [0, 9.7E-4]<a name="line.1310"></a>
<FONT color="green">1311</FONT>             * lnm[0]   [0, 0.692]<a name="line.1311"></a>
<FONT color="green">1312</FONT>             * ln2A*exp [0, 709]<a name="line.1312"></a>
<FONT color="green">1313</FONT>             */<a name="line.1313"></a>
<FONT color="green">1314</FONT>    <a name="line.1314"></a>
<FONT color="green">1315</FONT>            /* Compute the following sum:<a name="line.1315"></a>
<FONT color="green">1316</FONT>             * lnzb + lnm[1] + ln2B*exp + lnza + lnm[0] + ln2A*exp;<a name="line.1316"></a>
<FONT color="green">1317</FONT>             */<a name="line.1317"></a>
<FONT color="green">1318</FONT>    <a name="line.1318"></a>
<FONT color="green">1319</FONT>            //return lnzb + lnm[1] + ln2B*exp + lnza + lnm[0] + ln2A*exp;<a name="line.1319"></a>
<FONT color="green">1320</FONT>            double a = LN_2_A*exp;<a name="line.1320"></a>
<FONT color="green">1321</FONT>            double b = 0.0;<a name="line.1321"></a>
<FONT color="green">1322</FONT>            double c = a+lnm[0];<a name="line.1322"></a>
<FONT color="green">1323</FONT>            double d = -(c-a-lnm[0]);<a name="line.1323"></a>
<FONT color="green">1324</FONT>            a = c;<a name="line.1324"></a>
<FONT color="green">1325</FONT>            b = b + d;<a name="line.1325"></a>
<FONT color="green">1326</FONT>    <a name="line.1326"></a>
<FONT color="green">1327</FONT>            c = a + lnza;<a name="line.1327"></a>
<FONT color="green">1328</FONT>            d = -(c - a - lnza);<a name="line.1328"></a>
<FONT color="green">1329</FONT>            a = c;<a name="line.1329"></a>
<FONT color="green">1330</FONT>            b = b + d;<a name="line.1330"></a>
<FONT color="green">1331</FONT>    <a name="line.1331"></a>
<FONT color="green">1332</FONT>            c = a + LN_2_B*exp;<a name="line.1332"></a>
<FONT color="green">1333</FONT>            d = -(c - a - LN_2_B*exp);<a name="line.1333"></a>
<FONT color="green">1334</FONT>            a = c;<a name="line.1334"></a>
<FONT color="green">1335</FONT>            b = b + d;<a name="line.1335"></a>
<FONT color="green">1336</FONT>    <a name="line.1336"></a>
<FONT color="green">1337</FONT>            c = a + lnm[1];<a name="line.1337"></a>
<FONT color="green">1338</FONT>            d = -(c - a - lnm[1]);<a name="line.1338"></a>
<FONT color="green">1339</FONT>            a = c;<a name="line.1339"></a>
<FONT color="green">1340</FONT>            b = b + d;<a name="line.1340"></a>
<FONT color="green">1341</FONT>    <a name="line.1341"></a>
<FONT color="green">1342</FONT>            c = a + lnzb;<a name="line.1342"></a>
<FONT color="green">1343</FONT>            d = -(c - a - lnzb);<a name="line.1343"></a>
<FONT color="green">1344</FONT>            a = c;<a name="line.1344"></a>
<FONT color="green">1345</FONT>            b = b + d;<a name="line.1345"></a>
<FONT color="green">1346</FONT>    <a name="line.1346"></a>
<FONT color="green">1347</FONT>            if (hiPrec != null) {<a name="line.1347"></a>
<FONT color="green">1348</FONT>                hiPrec[0] = a;<a name="line.1348"></a>
<FONT color="green">1349</FONT>                hiPrec[1] = b;<a name="line.1349"></a>
<FONT color="green">1350</FONT>            }<a name="line.1350"></a>
<FONT color="green">1351</FONT>    <a name="line.1351"></a>
<FONT color="green">1352</FONT>            return a + b;<a name="line.1352"></a>
<FONT color="green">1353</FONT>        }<a name="line.1353"></a>
<FONT color="green">1354</FONT>    <a name="line.1354"></a>
<FONT color="green">1355</FONT>        /**<a name="line.1355"></a>
<FONT color="green">1356</FONT>         * Computes log(1 + x).<a name="line.1356"></a>
<FONT color="green">1357</FONT>         *<a name="line.1357"></a>
<FONT color="green">1358</FONT>         * @param x Number.<a name="line.1358"></a>
<FONT color="green">1359</FONT>         * @return {@code log(1 + x)}.<a name="line.1359"></a>
<FONT color="green">1360</FONT>         */<a name="line.1360"></a>
<FONT color="green">1361</FONT>        public static double log1p(final double x) {<a name="line.1361"></a>
<FONT color="green">1362</FONT>            if (x == -1) {<a name="line.1362"></a>
<FONT color="green">1363</FONT>                return Double.NEGATIVE_INFINITY;<a name="line.1363"></a>
<FONT color="green">1364</FONT>            }<a name="line.1364"></a>
<FONT color="green">1365</FONT>    <a name="line.1365"></a>
<FONT color="green">1366</FONT>            if (x == Double.POSITIVE_INFINITY) {<a name="line.1366"></a>
<FONT color="green">1367</FONT>                return Double.POSITIVE_INFINITY;<a name="line.1367"></a>
<FONT color="green">1368</FONT>            }<a name="line.1368"></a>
<FONT color="green">1369</FONT>    <a name="line.1369"></a>
<FONT color="green">1370</FONT>            if (x &gt; 1e-6 ||<a name="line.1370"></a>
<FONT color="green">1371</FONT>                x &lt; -1e-6) {<a name="line.1371"></a>
<FONT color="green">1372</FONT>                final double xpa = 1 + x;<a name="line.1372"></a>
<FONT color="green">1373</FONT>                final double xpb = -(xpa - 1 - x);<a name="line.1373"></a>
<FONT color="green">1374</FONT>    <a name="line.1374"></a>
<FONT color="green">1375</FONT>                final double[] hiPrec = new double[2];<a name="line.1375"></a>
<FONT color="green">1376</FONT>                final double lores = log(xpa, hiPrec);<a name="line.1376"></a>
<FONT color="green">1377</FONT>                if (Double.isInfinite(lores)) { // Don't allow this to be converted to NaN<a name="line.1377"></a>
<FONT color="green">1378</FONT>                    return lores;<a name="line.1378"></a>
<FONT color="green">1379</FONT>                }<a name="line.1379"></a>
<FONT color="green">1380</FONT>    <a name="line.1380"></a>
<FONT color="green">1381</FONT>                // Do a taylor series expansion around xpa:<a name="line.1381"></a>
<FONT color="green">1382</FONT>                //   f(x+y) = f(x) + f'(x) y + f''(x)/2 y^2<a name="line.1382"></a>
<FONT color="green">1383</FONT>                final double fx1 = xpb / xpa;<a name="line.1383"></a>
<FONT color="green">1384</FONT>                final double epsilon = 0.5 * fx1 + 1;<a name="line.1384"></a>
<FONT color="green">1385</FONT>                return epsilon * fx1 + hiPrec[1] + hiPrec[0];<a name="line.1385"></a>
<FONT color="green">1386</FONT>            } else {<a name="line.1386"></a>
<FONT color="green">1387</FONT>                // Value is small |x| &lt; 1e6, do a Taylor series centered on 1.<a name="line.1387"></a>
<FONT color="green">1388</FONT>                final double y = (x * F_1_3 - F_1_2) * x + 1;<a name="line.1388"></a>
<FONT color="green">1389</FONT>                return y * x;<a name="line.1389"></a>
<FONT color="green">1390</FONT>            }<a name="line.1390"></a>
<FONT color="green">1391</FONT>        }<a name="line.1391"></a>
<FONT color="green">1392</FONT>    <a name="line.1392"></a>
<FONT color="green">1393</FONT>        /** Compute the base 10 logarithm.<a name="line.1393"></a>
<FONT color="green">1394</FONT>         * @param x a number<a name="line.1394"></a>
<FONT color="green">1395</FONT>         * @return log10(x)<a name="line.1395"></a>
<FONT color="green">1396</FONT>         */<a name="line.1396"></a>
<FONT color="green">1397</FONT>        public static double log10(final double x) {<a name="line.1397"></a>
<FONT color="green">1398</FONT>            final double hiPrec[] = new double[2];<a name="line.1398"></a>
<FONT color="green">1399</FONT>    <a name="line.1399"></a>
<FONT color="green">1400</FONT>            final double lores = log(x, hiPrec);<a name="line.1400"></a>
<FONT color="green">1401</FONT>            if (Double.isInfinite(lores)){ // don't allow this to be converted to NaN<a name="line.1401"></a>
<FONT color="green">1402</FONT>                return lores;<a name="line.1402"></a>
<FONT color="green">1403</FONT>            }<a name="line.1403"></a>
<FONT color="green">1404</FONT>    <a name="line.1404"></a>
<FONT color="green">1405</FONT>            final double tmp = hiPrec[0] * HEX_40000000;<a name="line.1405"></a>
<FONT color="green">1406</FONT>            final double lna = hiPrec[0] + tmp - tmp;<a name="line.1406"></a>
<FONT color="green">1407</FONT>            final double lnb = hiPrec[0] - lna + hiPrec[1];<a name="line.1407"></a>
<FONT color="green">1408</FONT>    <a name="line.1408"></a>
<FONT color="green">1409</FONT>            final double rln10a = 0.4342944622039795;<a name="line.1409"></a>
<FONT color="green">1410</FONT>            final double rln10b = 1.9699272335463627E-8;<a name="line.1410"></a>
<FONT color="green">1411</FONT>    <a name="line.1411"></a>
<FONT color="green">1412</FONT>            return rln10b * lnb + rln10b * lna + rln10a * lnb + rln10a * lna;<a name="line.1412"></a>
<FONT color="green">1413</FONT>        }<a name="line.1413"></a>
<FONT color="green">1414</FONT>    <a name="line.1414"></a>
<FONT color="green">1415</FONT>        /**<a name="line.1415"></a>
<FONT color="green">1416</FONT>         * Computes the &lt;a href="http://mathworld.wolfram.com/Logarithm.html"&gt;<a name="line.1416"></a>
<FONT color="green">1417</FONT>         * logarithm&lt;/a&gt; in a given base.<a name="line.1417"></a>
<FONT color="green">1418</FONT>         *<a name="line.1418"></a>
<FONT color="green">1419</FONT>         * Returns {@code NaN} if either argument is negative.<a name="line.1419"></a>
<FONT color="green">1420</FONT>         * If {@code base} is 0 and {@code x} is positive, 0 is returned.<a name="line.1420"></a>
<FONT color="green">1421</FONT>         * If {@code base} is positive and {@code x} is 0,<a name="line.1421"></a>
<FONT color="green">1422</FONT>         * {@code Double.NEGATIVE_INFINITY} is returned.<a name="line.1422"></a>
<FONT color="green">1423</FONT>         * If both arguments are 0, the result is {@code NaN}.<a name="line.1423"></a>
<FONT color="green">1424</FONT>         *<a name="line.1424"></a>
<FONT color="green">1425</FONT>         * @param base Base of the logarithm, must be greater than 0.<a name="line.1425"></a>
<FONT color="green">1426</FONT>         * @param x Argument, must be greater than 0.<a name="line.1426"></a>
<FONT color="green">1427</FONT>         * @return the value of the logarithm, i.e. the number {@code y} such that<a name="line.1427"></a>
<FONT color="green">1428</FONT>         * &lt;code&gt;base&lt;sup&gt;y&lt;/sup&gt; = x&lt;/code&gt;.<a name="line.1428"></a>
<FONT color="green">1429</FONT>         * @since 1.2 (previously in {@code MathUtils}, moved as of version 3.0)<a name="line.1429"></a>
<FONT color="green">1430</FONT>         */<a name="line.1430"></a>
<FONT color="green">1431</FONT>        public static double log(double base, double x) {<a name="line.1431"></a>
<FONT color="green">1432</FONT>            return log(x) / log(base);<a name="line.1432"></a>
<FONT color="green">1433</FONT>        }<a name="line.1433"></a>
<FONT color="green">1434</FONT>    <a name="line.1434"></a>
<FONT color="green">1435</FONT>        /**<a name="line.1435"></a>
<FONT color="green">1436</FONT>         * Power function.  Compute x^y.<a name="line.1436"></a>
<FONT color="green">1437</FONT>         *<a name="line.1437"></a>
<FONT color="green">1438</FONT>         * @param x   a double<a name="line.1438"></a>
<FONT color="green">1439</FONT>         * @param y   a double<a name="line.1439"></a>
<FONT color="green">1440</FONT>         * @return double<a name="line.1440"></a>
<FONT color="green">1441</FONT>         */<a name="line.1441"></a>
<FONT color="green">1442</FONT>        public static double pow(double x, double y) {<a name="line.1442"></a>
<FONT color="green">1443</FONT>            final double lns[] = new double[2];<a name="line.1443"></a>
<FONT color="green">1444</FONT>    <a name="line.1444"></a>
<FONT color="green">1445</FONT>            if (y == 0.0) {<a name="line.1445"></a>
<FONT color="green">1446</FONT>                return 1.0;<a name="line.1446"></a>
<FONT color="green">1447</FONT>            }<a name="line.1447"></a>
<FONT color="green">1448</FONT>    <a name="line.1448"></a>
<FONT color="green">1449</FONT>            if (x != x) { // X is NaN<a name="line.1449"></a>
<FONT color="green">1450</FONT>                return x;<a name="line.1450"></a>
<FONT color="green">1451</FONT>            }<a name="line.1451"></a>
<FONT color="green">1452</FONT>    <a name="line.1452"></a>
<FONT color="green">1453</FONT>    <a name="line.1453"></a>
<FONT color="green">1454</FONT>            if (x == 0) {<a name="line.1454"></a>
<FONT color="green">1455</FONT>                long bits = Double.doubleToLongBits(x);<a name="line.1455"></a>
<FONT color="green">1456</FONT>                if ((bits &amp; 0x8000000000000000L) != 0) {<a name="line.1456"></a>
<FONT color="green">1457</FONT>                    // -zero<a name="line.1457"></a>
<FONT color="green">1458</FONT>                    long yi = (long) y;<a name="line.1458"></a>
<FONT color="green">1459</FONT>    <a name="line.1459"></a>
<FONT color="green">1460</FONT>                    if (y &lt; 0 &amp;&amp; y == yi &amp;&amp; (yi &amp; 1) == 1) {<a name="line.1460"></a>
<FONT color="green">1461</FONT>                        return Double.NEGATIVE_INFINITY;<a name="line.1461"></a>
<FONT color="green">1462</FONT>                    }<a name="line.1462"></a>
<FONT color="green">1463</FONT>    <a name="line.1463"></a>
<FONT color="green">1464</FONT>                    if (y &gt; 0 &amp;&amp; y == yi &amp;&amp; (yi &amp; 1) == 1) {<a name="line.1464"></a>
<FONT color="green">1465</FONT>                        return -0.0;<a name="line.1465"></a>
<FONT color="green">1466</FONT>                    }<a name="line.1466"></a>
<FONT color="green">1467</FONT>                }<a name="line.1467"></a>
<FONT color="green">1468</FONT>    <a name="line.1468"></a>
<FONT color="green">1469</FONT>                if (y &lt; 0) {<a name="line.1469"></a>
<FONT color="green">1470</FONT>                    return Double.POSITIVE_INFINITY;<a name="line.1470"></a>
<FONT color="green">1471</FONT>                }<a name="line.1471"></a>
<FONT color="green">1472</FONT>                if (y &gt; 0) {<a name="line.1472"></a>
<FONT color="green">1473</FONT>                    return 0.0;<a name="line.1473"></a>
<FONT color="green">1474</FONT>                }<a name="line.1474"></a>
<FONT color="green">1475</FONT>    <a name="line.1475"></a>
<FONT color="green">1476</FONT>                return Double.NaN;<a name="line.1476"></a>
<FONT color="green">1477</FONT>            }<a name="line.1477"></a>
<FONT color="green">1478</FONT>    <a name="line.1478"></a>
<FONT color="green">1479</FONT>            if (x == Double.POSITIVE_INFINITY) {<a name="line.1479"></a>
<FONT color="green">1480</FONT>                if (y != y) { // y is NaN<a name="line.1480"></a>
<FONT color="green">1481</FONT>                    return y;<a name="line.1481"></a>
<FONT color="green">1482</FONT>                }<a name="line.1482"></a>
<FONT color="green">1483</FONT>                if (y &lt; 0.0) {<a name="line.1483"></a>
<FONT color="green">1484</FONT>                    return 0.0;<a name="line.1484"></a>
<FONT color="green">1485</FONT>                } else {<a name="line.1485"></a>
<FONT color="green">1486</FONT>                    return Double.POSITIVE_INFINITY;<a name="line.1486"></a>
<FONT color="green">1487</FONT>                }<a name="line.1487"></a>
<FONT color="green">1488</FONT>            }<a name="line.1488"></a>
<FONT color="green">1489</FONT>    <a name="line.1489"></a>
<FONT color="green">1490</FONT>            if (y == Double.POSITIVE_INFINITY) {<a name="line.1490"></a>
<FONT color="green">1491</FONT>                if (x * x == 1.0) {<a name="line.1491"></a>
<FONT color="green">1492</FONT>                    return Double.NaN;<a name="line.1492"></a>
<FONT color="green">1493</FONT>                }<a name="line.1493"></a>
<FONT color="green">1494</FONT>    <a name="line.1494"></a>
<FONT color="green">1495</FONT>                if (x * x &gt; 1.0) {<a name="line.1495"></a>
<FONT color="green">1496</FONT>                    return Double.POSITIVE_INFINITY;<a name="line.1496"></a>
<FONT color="green">1497</FONT>                } else {<a name="line.1497"></a>
<FONT color="green">1498</FONT>                    return 0.0;<a name="line.1498"></a>
<FONT color="green">1499</FONT>                }<a name="line.1499"></a>
<FONT color="green">1500</FONT>            }<a name="line.1500"></a>
<FONT color="green">1501</FONT>    <a name="line.1501"></a>
<FONT color="green">1502</FONT>            if (x == Double.NEGATIVE_INFINITY) {<a name="line.1502"></a>
<FONT color="green">1503</FONT>                if (y != y) { // y is NaN<a name="line.1503"></a>
<FONT color="green">1504</FONT>                    return y;<a name="line.1504"></a>
<FONT color="green">1505</FONT>                }<a name="line.1505"></a>
<FONT color="green">1506</FONT>    <a name="line.1506"></a>
<FONT color="green">1507</FONT>                if (y &lt; 0) {<a name="line.1507"></a>
<FONT color="green">1508</FONT>                    long yi = (long) y;<a name="line.1508"></a>
<FONT color="green">1509</FONT>                    if (y == yi &amp;&amp; (yi &amp; 1) == 1) {<a name="line.1509"></a>
<FONT color="green">1510</FONT>                        return -0.0;<a name="line.1510"></a>
<FONT color="green">1511</FONT>                    }<a name="line.1511"></a>
<FONT color="green">1512</FONT>    <a name="line.1512"></a>
<FONT color="green">1513</FONT>                    return 0.0;<a name="line.1513"></a>
<FONT color="green">1514</FONT>                }<a name="line.1514"></a>
<FONT color="green">1515</FONT>    <a name="line.1515"></a>
<FONT color="green">1516</FONT>                if (y &gt; 0)  {<a name="line.1516"></a>
<FONT color="green">1517</FONT>                    long yi = (long) y;<a name="line.1517"></a>
<FONT color="green">1518</FONT>                    if (y == yi &amp;&amp; (yi &amp; 1) == 1) {<a name="line.1518"></a>
<FONT color="green">1519</FONT>                        return Double.NEGATIVE_INFINITY;<a name="line.1519"></a>
<FONT color="green">1520</FONT>                    }<a name="line.1520"></a>
<FONT color="green">1521</FONT>    <a name="line.1521"></a>
<FONT color="green">1522</FONT>                    return Double.POSITIVE_INFINITY;<a name="line.1522"></a>
<FONT color="green">1523</FONT>                }<a name="line.1523"></a>
<FONT color="green">1524</FONT>            }<a name="line.1524"></a>
<FONT color="green">1525</FONT>    <a name="line.1525"></a>
<FONT color="green">1526</FONT>            if (y == Double.NEGATIVE_INFINITY) {<a name="line.1526"></a>
<FONT color="green">1527</FONT>    <a name="line.1527"></a>
<FONT color="green">1528</FONT>                if (x * x == 1.0) {<a name="line.1528"></a>
<FONT color="green">1529</FONT>                    return Double.NaN;<a name="line.1529"></a>
<FONT color="green">1530</FONT>                }<a name="line.1530"></a>
<FONT color="green">1531</FONT>    <a name="line.1531"></a>
<FONT color="green">1532</FONT>                if (x * x &lt; 1.0) {<a name="line.1532"></a>
<FONT color="green">1533</FONT>                    return Double.POSITIVE_INFINITY;<a name="line.1533"></a>
<FONT color="green">1534</FONT>                } else {<a name="line.1534"></a>
<FONT color="green">1535</FONT>                    return 0.0;<a name="line.1535"></a>
<FONT color="green">1536</FONT>                }<a name="line.1536"></a>
<FONT color="green">1537</FONT>            }<a name="line.1537"></a>
<FONT color="green">1538</FONT>    <a name="line.1538"></a>
<FONT color="green">1539</FONT>            /* Handle special case x&lt;0 */<a name="line.1539"></a>
<FONT color="green">1540</FONT>            if (x &lt; 0) {<a name="line.1540"></a>
<FONT color="green">1541</FONT>                // y is an even integer in this case<a name="line.1541"></a>
<FONT color="green">1542</FONT>                if (y &gt;= TWO_POWER_53 || y &lt;= -TWO_POWER_53) {<a name="line.1542"></a>
<FONT color="green">1543</FONT>                    return pow(-x, y);<a name="line.1543"></a>
<FONT color="green">1544</FONT>                }<a name="line.1544"></a>
<FONT color="green">1545</FONT>    <a name="line.1545"></a>
<FONT color="green">1546</FONT>                if (y == (long) y) {<a name="line.1546"></a>
<FONT color="green">1547</FONT>                    // If y is an integer<a name="line.1547"></a>
<FONT color="green">1548</FONT>                    return ((long)y &amp; 1) == 0 ? pow(-x, y) : -pow(-x, y);<a name="line.1548"></a>
<FONT color="green">1549</FONT>                } else {<a name="line.1549"></a>
<FONT color="green">1550</FONT>                    return Double.NaN;<a name="line.1550"></a>
<FONT color="green">1551</FONT>                }<a name="line.1551"></a>
<FONT color="green">1552</FONT>            }<a name="line.1552"></a>
<FONT color="green">1553</FONT>    <a name="line.1553"></a>
<FONT color="green">1554</FONT>            /* Split y into ya and yb such that y = ya+yb */<a name="line.1554"></a>
<FONT color="green">1555</FONT>            double ya;<a name="line.1555"></a>
<FONT color="green">1556</FONT>            double yb;<a name="line.1556"></a>
<FONT color="green">1557</FONT>            if (y &lt; 8e298 &amp;&amp; y &gt; -8e298) {<a name="line.1557"></a>
<FONT color="green">1558</FONT>                double tmp1 = y * HEX_40000000;<a name="line.1558"></a>
<FONT color="green">1559</FONT>                ya = y + tmp1 - tmp1;<a name="line.1559"></a>
<FONT color="green">1560</FONT>                yb = y - ya;<a name="line.1560"></a>
<FONT color="green">1561</FONT>            } else {<a name="line.1561"></a>
<FONT color="green">1562</FONT>                double tmp1 = y * 9.31322574615478515625E-10;<a name="line.1562"></a>
<FONT color="green">1563</FONT>                double tmp2 = tmp1 * 9.31322574615478515625E-10;<a name="line.1563"></a>
<FONT color="green">1564</FONT>                ya = (tmp1 + tmp2 - tmp1) * HEX_40000000 * HEX_40000000;<a name="line.1564"></a>
<FONT color="green">1565</FONT>                yb = y - ya;<a name="line.1565"></a>
<FONT color="green">1566</FONT>            }<a name="line.1566"></a>
<FONT color="green">1567</FONT>    <a name="line.1567"></a>
<FONT color="green">1568</FONT>            /* Compute ln(x) */<a name="line.1568"></a>
<FONT color="green">1569</FONT>            final double lores = log(x, lns);<a name="line.1569"></a>
<FONT color="green">1570</FONT>            if (Double.isInfinite(lores)){ // don't allow this to be converted to NaN<a name="line.1570"></a>
<FONT color="green">1571</FONT>                return lores;<a name="line.1571"></a>
<FONT color="green">1572</FONT>            }<a name="line.1572"></a>
<FONT color="green">1573</FONT>    <a name="line.1573"></a>
<FONT color="green">1574</FONT>            double lna = lns[0];<a name="line.1574"></a>
<FONT color="green">1575</FONT>            double lnb = lns[1];<a name="line.1575"></a>
<FONT color="green">1576</FONT>    <a name="line.1576"></a>
<FONT color="green">1577</FONT>            /* resplit lns */<a name="line.1577"></a>
<FONT color="green">1578</FONT>            double tmp1 = lna * HEX_40000000;<a name="line.1578"></a>
<FONT color="green">1579</FONT>            double tmp2 = lna + tmp1 - tmp1;<a name="line.1579"></a>
<FONT color="green">1580</FONT>            lnb += lna - tmp2;<a name="line.1580"></a>
<FONT color="green">1581</FONT>            lna = tmp2;<a name="line.1581"></a>
<FONT color="green">1582</FONT>    <a name="line.1582"></a>
<FONT color="green">1583</FONT>            // y*ln(x) = (aa+ab)<a name="line.1583"></a>
<FONT color="green">1584</FONT>            final double aa = lna * ya;<a name="line.1584"></a>
<FONT color="green">1585</FONT>            final double ab = lna * yb + lnb * ya + lnb * yb;<a name="line.1585"></a>
<FONT color="green">1586</FONT>    <a name="line.1586"></a>
<FONT color="green">1587</FONT>            lna = aa+ab;<a name="line.1587"></a>
<FONT color="green">1588</FONT>            lnb = -(lna - aa - ab);<a name="line.1588"></a>
<FONT color="green">1589</FONT>    <a name="line.1589"></a>
<FONT color="green">1590</FONT>            double z = 1.0 / 120.0;<a name="line.1590"></a>
<FONT color="green">1591</FONT>            z = z * lnb + (1.0 / 24.0);<a name="line.1591"></a>
<FONT color="green">1592</FONT>            z = z * lnb + (1.0 / 6.0);<a name="line.1592"></a>
<FONT color="green">1593</FONT>            z = z * lnb + 0.5;<a name="line.1593"></a>
<FONT color="green">1594</FONT>            z = z * lnb + 1.0;<a name="line.1594"></a>
<FONT color="green">1595</FONT>            z = z * lnb;<a name="line.1595"></a>
<FONT color="green">1596</FONT>    <a name="line.1596"></a>
<FONT color="green">1597</FONT>            final double result = exp(lna, z, null);<a name="line.1597"></a>
<FONT color="green">1598</FONT>            //result = result + result * z;<a name="line.1598"></a>
<FONT color="green">1599</FONT>            return result;<a name="line.1599"></a>
<FONT color="green">1600</FONT>        }<a name="line.1600"></a>
<FONT color="green">1601</FONT>    <a name="line.1601"></a>
<FONT color="green">1602</FONT>    <a name="line.1602"></a>
<FONT color="green">1603</FONT>        /**<a name="line.1603"></a>
<FONT color="green">1604</FONT>         * Raise a double to an int power.<a name="line.1604"></a>
<FONT color="green">1605</FONT>         *<a name="line.1605"></a>
<FONT color="green">1606</FONT>         * @param d Number to raise.<a name="line.1606"></a>
<FONT color="green">1607</FONT>         * @param e Exponent.<a name="line.1607"></a>
<FONT color="green">1608</FONT>         * @return d&lt;sup&gt;e&lt;/sup&gt;<a name="line.1608"></a>
<FONT color="green">1609</FONT>         * @since 3.1<a name="line.1609"></a>
<FONT color="green">1610</FONT>         */<a name="line.1610"></a>
<FONT color="green">1611</FONT>        public static double pow(double d, int e) {<a name="line.1611"></a>
<FONT color="green">1612</FONT>    <a name="line.1612"></a>
<FONT color="green">1613</FONT>            if (e == 0) {<a name="line.1613"></a>
<FONT color="green">1614</FONT>                return 1.0;<a name="line.1614"></a>
<FONT color="green">1615</FONT>            } else if (e &lt; 0) {<a name="line.1615"></a>
<FONT color="green">1616</FONT>                e = -e;<a name="line.1616"></a>
<FONT color="green">1617</FONT>                d = 1.0 / d;<a name="line.1617"></a>
<FONT color="green">1618</FONT>            }<a name="line.1618"></a>
<FONT color="green">1619</FONT>    <a name="line.1619"></a>
<FONT color="green">1620</FONT>            // split d as two 26 bits numbers<a name="line.1620"></a>
<FONT color="green">1621</FONT>            // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties<a name="line.1621"></a>
<FONT color="green">1622</FONT>            final int splitFactor = 0x8000001;<a name="line.1622"></a>
<FONT color="green">1623</FONT>            final double cd       = splitFactor * d;<a name="line.1623"></a>
<FONT color="green">1624</FONT>            final double d1High   = cd - (cd - d);<a name="line.1624"></a>
<FONT color="green">1625</FONT>            final double d1Low    = d - d1High;<a name="line.1625"></a>
<FONT color="green">1626</FONT>    <a name="line.1626"></a>
<FONT color="green">1627</FONT>            // prepare result<a name="line.1627"></a>
<FONT color="green">1628</FONT>            double resultHigh = 1;<a name="line.1628"></a>
<FONT color="green">1629</FONT>            double resultLow  = 0;<a name="line.1629"></a>
<FONT color="green">1630</FONT>    <a name="line.1630"></a>
<FONT color="green">1631</FONT>            // d^(2p)<a name="line.1631"></a>
<FONT color="green">1632</FONT>            double d2p     = d;<a name="line.1632"></a>
<FONT color="green">1633</FONT>            double d2pHigh = d1High;<a name="line.1633"></a>
<FONT color="green">1634</FONT>            double d2pLow  = d1Low;<a name="line.1634"></a>
<FONT color="green">1635</FONT>    <a name="line.1635"></a>
<FONT color="green">1636</FONT>            while (e != 0) {<a name="line.1636"></a>
<FONT color="green">1637</FONT>    <a name="line.1637"></a>
<FONT color="green">1638</FONT>                if ((e &amp; 0x1) != 0) {<a name="line.1638"></a>
<FONT color="green">1639</FONT>                    // accurate multiplication result = result * d^(2p) using Veltkamp TwoProduct algorithm<a name="line.1639"></a>
<FONT color="green">1640</FONT>                    // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties<a name="line.1640"></a>
<FONT color="green">1641</FONT>                    final double tmpHigh = resultHigh * d2p;<a name="line.1641"></a>
<FONT color="green">1642</FONT>                    final double cRH     = splitFactor * resultHigh;<a name="line.1642"></a>
<FONT color="green">1643</FONT>                    final double rHH     = cRH - (cRH - resultHigh);<a name="line.1643"></a>
<FONT color="green">1644</FONT>                    final double rHL     = resultHigh - rHH;<a name="line.1644"></a>
<FONT color="green">1645</FONT>                    final double tmpLow  = rHL * d2pLow - (((tmpHigh - rHH * d2pHigh) - rHL * d2pHigh) - rHH * d2pLow);<a name="line.1645"></a>
<FONT color="green">1646</FONT>                    resultHigh = tmpHigh;<a name="line.1646"></a>
<FONT color="green">1647</FONT>                    resultLow  = resultLow * d2p + tmpLow;<a name="line.1647"></a>
<FONT color="green">1648</FONT>                }<a name="line.1648"></a>
<FONT color="green">1649</FONT>    <a name="line.1649"></a>
<FONT color="green">1650</FONT>                // accurate squaring d^(2(p+1)) = d^(2p) * d^(2p) using Veltkamp TwoProduct algorithm<a name="line.1650"></a>
<FONT color="green">1651</FONT>                // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties<a name="line.1651"></a>
<FONT color="green">1652</FONT>                final double tmpHigh = d2pHigh * d2p;<a name="line.1652"></a>
<FONT color="green">1653</FONT>                final double cD2pH   = splitFactor * d2pHigh;<a name="line.1653"></a>
<FONT color="green">1654</FONT>                final double d2pHH   = cD2pH - (cD2pH - d2pHigh);<a name="line.1654"></a>
<FONT color="green">1655</FONT>                final double d2pHL   = d2pHigh - d2pHH;<a name="line.1655"></a>
<FONT color="green">1656</FONT>                final double tmpLow  = d2pHL * d2pLow - (((tmpHigh - d2pHH * d2pHigh) - d2pHL * d2pHigh) - d2pHH * d2pLow);<a name="line.1656"></a>
<FONT color="green">1657</FONT>                final double cTmpH   = splitFactor * tmpHigh;<a name="line.1657"></a>
<FONT color="green">1658</FONT>                d2pHigh = cTmpH - (cTmpH - tmpHigh);<a name="line.1658"></a>
<FONT color="green">1659</FONT>                d2pLow  = d2pLow * d2p + tmpLow + (tmpHigh - d2pHigh);<a name="line.1659"></a>
<FONT color="green">1660</FONT>                d2p     = d2pHigh + d2pLow;<a name="line.1660"></a>
<FONT color="green">1661</FONT>    <a name="line.1661"></a>
<FONT color="green">1662</FONT>                e = e &gt;&gt; 1;<a name="line.1662"></a>
<FONT color="green">1663</FONT>    <a name="line.1663"></a>
<FONT color="green">1664</FONT>            }<a name="line.1664"></a>
<FONT color="green">1665</FONT>    <a name="line.1665"></a>
<FONT color="green">1666</FONT>            return resultHigh + resultLow;<a name="line.1666"></a>
<FONT color="green">1667</FONT>    <a name="line.1667"></a>
<FONT color="green">1668</FONT>        }<a name="line.1668"></a>
<FONT color="green">1669</FONT>    <a name="line.1669"></a>
<FONT color="green">1670</FONT>        /**<a name="line.1670"></a>
<FONT color="green">1671</FONT>         *  Computes sin(x) - x, where |x| &lt; 1/16.<a name="line.1671"></a>
<FONT color="green">1672</FONT>         *  Use a Remez polynomial approximation.<a name="line.1672"></a>
<FONT color="green">1673</FONT>         *  @param x a number smaller than 1/16<a name="line.1673"></a>
<FONT color="green">1674</FONT>         *  @return sin(x) - x<a name="line.1674"></a>
<FONT color="green">1675</FONT>         */<a name="line.1675"></a>
<FONT color="green">1676</FONT>        private static double polySine(final double x)<a name="line.1676"></a>
<FONT color="green">1677</FONT>        {<a name="line.1677"></a>
<FONT color="green">1678</FONT>            double x2 = x*x;<a name="line.1678"></a>
<FONT color="green">1679</FONT>    <a name="line.1679"></a>
<FONT color="green">1680</FONT>            double p = 2.7553817452272217E-6;<a name="line.1680"></a>
<FONT color="green">1681</FONT>            p = p * x2 + -1.9841269659586505E-4;<a name="line.1681"></a>
<FONT color="green">1682</FONT>            p = p * x2 + 0.008333333333329196;<a name="line.1682"></a>
<FONT color="green">1683</FONT>            p = p * x2 + -0.16666666666666666;<a name="line.1683"></a>
<FONT color="green">1684</FONT>            //p *= x2;<a name="line.1684"></a>
<FONT color="green">1685</FONT>            //p *= x;<a name="line.1685"></a>
<FONT color="green">1686</FONT>            p = p * x2 * x;<a name="line.1686"></a>
<FONT color="green">1687</FONT>    <a name="line.1687"></a>
<FONT color="green">1688</FONT>            return p;<a name="line.1688"></a>
<FONT color="green">1689</FONT>        }<a name="line.1689"></a>
<FONT color="green">1690</FONT>    <a name="line.1690"></a>
<FONT color="green">1691</FONT>        /**<a name="line.1691"></a>
<FONT color="green">1692</FONT>         *  Computes cos(x) - 1, where |x| &lt; 1/16.<a name="line.1692"></a>
<FONT color="green">1693</FONT>         *  Use a Remez polynomial approximation.<a name="line.1693"></a>
<FONT color="green">1694</FONT>         *  @param x a number smaller than 1/16<a name="line.1694"></a>
<FONT color="green">1695</FONT>         *  @return cos(x) - 1<a name="line.1695"></a>
<FONT color="green">1696</FONT>         */<a name="line.1696"></a>
<FONT color="green">1697</FONT>        private static double polyCosine(double x) {<a name="line.1697"></a>
<FONT color="green">1698</FONT>            double x2 = x*x;<a name="line.1698"></a>
<FONT color="green">1699</FONT>    <a name="line.1699"></a>
<FONT color="green">1700</FONT>            double p = 2.479773539153719E-5;<a name="line.1700"></a>
<FONT color="green">1701</FONT>            p = p * x2 + -0.0013888888689039883;<a name="line.1701"></a>
<FONT color="green">1702</FONT>            p = p * x2 + 0.041666666666621166;<a name="line.1702"></a>
<FONT color="green">1703</FONT>            p = p * x2 + -0.49999999999999994;<a name="line.1703"></a>
<FONT color="green">1704</FONT>            p *= x2;<a name="line.1704"></a>
<FONT color="green">1705</FONT>    <a name="line.1705"></a>
<FONT color="green">1706</FONT>            return p;<a name="line.1706"></a>
<FONT color="green">1707</FONT>        }<a name="line.1707"></a>
<FONT color="green">1708</FONT>    <a name="line.1708"></a>
<FONT color="green">1709</FONT>        /**<a name="line.1709"></a>
<FONT color="green">1710</FONT>         *  Compute sine over the first quadrant (0 &lt; x &lt; pi/2).<a name="line.1710"></a>
<FONT color="green">1711</FONT>         *  Use combination of table lookup and rational polynomial expansion.<a name="line.1711"></a>
<FONT color="green">1712</FONT>         *  @param xa number from which sine is requested<a name="line.1712"></a>
<FONT color="green">1713</FONT>         *  @param xb extra bits for x (may be 0.0)<a name="line.1713"></a>
<FONT color="green">1714</FONT>         *  @return sin(xa + xb)<a name="line.1714"></a>
<FONT color="green">1715</FONT>         */<a name="line.1715"></a>
<FONT color="green">1716</FONT>        private static double sinQ(double xa, double xb) {<a name="line.1716"></a>
<FONT color="green">1717</FONT>            int idx = (int) ((xa * 8.0) + 0.5);<a name="line.1717"></a>
<FONT color="green">1718</FONT>            final double epsilon = xa - EIGHTHS[idx]; //idx*0.125;<a name="line.1718"></a>
<FONT color="green">1719</FONT>    <a name="line.1719"></a>
<FONT color="green">1720</FONT>            // Table lookups<a name="line.1720"></a>
<FONT color="green">1721</FONT>            final double sintA = SINE_TABLE_A[idx];<a name="line.1721"></a>
<FONT color="green">1722</FONT>            final double sintB = SINE_TABLE_B[idx];<a name="line.1722"></a>
<FONT color="green">1723</FONT>            final double costA = COSINE_TABLE_A[idx];<a name="line.1723"></a>
<FONT color="green">1724</FONT>            final double costB = COSINE_TABLE_B[idx];<a name="line.1724"></a>
<FONT color="green">1725</FONT>    <a name="line.1725"></a>
<FONT color="green">1726</FONT>            // Polynomial eval of sin(epsilon), cos(epsilon)<a name="line.1726"></a>
<FONT color="green">1727</FONT>            double sinEpsA = epsilon;<a name="line.1727"></a>
<FONT color="green">1728</FONT>            double sinEpsB = polySine(epsilon);<a name="line.1728"></a>
<FONT color="green">1729</FONT>            final double cosEpsA = 1.0;<a name="line.1729"></a>
<FONT color="green">1730</FONT>            final double cosEpsB = polyCosine(epsilon);<a name="line.1730"></a>
<FONT color="green">1731</FONT>    <a name="line.1731"></a>
<FONT color="green">1732</FONT>            // Split epsilon   xa + xb = x<a name="line.1732"></a>
<FONT color="green">1733</FONT>            final double temp = sinEpsA * HEX_40000000;<a name="line.1733"></a>
<FONT color="green">1734</FONT>            double temp2 = (sinEpsA + temp) - temp;<a name="line.1734"></a>
<FONT color="green">1735</FONT>            sinEpsB +=  sinEpsA - temp2;<a name="line.1735"></a>
<FONT color="green">1736</FONT>            sinEpsA = temp2;<a name="line.1736"></a>
<FONT color="green">1737</FONT>    <a name="line.1737"></a>
<FONT color="green">1738</FONT>            /* Compute sin(x) by angle addition formula */<a name="line.1738"></a>
<FONT color="green">1739</FONT>            double result;<a name="line.1739"></a>
<FONT color="green">1740</FONT>    <a name="line.1740"></a>
<FONT color="green">1741</FONT>            /* Compute the following sum:<a name="line.1741"></a>
<FONT color="green">1742</FONT>             *<a name="line.1742"></a>
<FONT color="green">1743</FONT>             * result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +<a name="line.1743"></a>
<FONT color="green">1744</FONT>             *          sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;<a name="line.1744"></a>
<FONT color="green">1745</FONT>             *<a name="line.1745"></a>
<FONT color="green">1746</FONT>             * Ranges of elements<a name="line.1746"></a>
<FONT color="green">1747</FONT>             *<a name="line.1747"></a>
<FONT color="green">1748</FONT>             * xxxtA   0            PI/2<a name="line.1748"></a>
<FONT color="green">1749</FONT>             * xxxtB   -1.5e-9      1.5e-9<a name="line.1749"></a>
<FONT color="green">1750</FONT>             * sinEpsA -0.0625      0.0625<a name="line.1750"></a>
<FONT color="green">1751</FONT>             * sinEpsB -6e-11       6e-11<a name="line.1751"></a>
<FONT color="green">1752</FONT>             * cosEpsA  1.0<a name="line.1752"></a>
<FONT color="green">1753</FONT>             * cosEpsB  0           -0.0625<a name="line.1753"></a>
<FONT color="green">1754</FONT>             *<a name="line.1754"></a>
<FONT color="green">1755</FONT>             */<a name="line.1755"></a>
<FONT color="green">1756</FONT>    <a name="line.1756"></a>
<FONT color="green">1757</FONT>            //result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +<a name="line.1757"></a>
<FONT color="green">1758</FONT>            //          sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;<a name="line.1758"></a>
<FONT color="green">1759</FONT>    <a name="line.1759"></a>
<FONT color="green">1760</FONT>            //result = sintA + sintA*cosEpsB + sintB + sintB * cosEpsB;<a name="line.1760"></a>
<FONT color="green">1761</FONT>            //result += costA*sinEpsA + costA*sinEpsB + costB*sinEpsA + costB * sinEpsB;<a name="line.1761"></a>
<FONT color="green">1762</FONT>            double a = 0;<a name="line.1762"></a>
<FONT color="green">1763</FONT>            double b = 0;<a name="line.1763"></a>
<FONT color="green">1764</FONT>    <a name="line.1764"></a>
<FONT color="green">1765</FONT>            double t = sintA;<a name="line.1765"></a>
<FONT color="green">1766</FONT>            double c = a + t;<a name="line.1766"></a>
<FONT color="green">1767</FONT>            double d = -(c - a - t);<a name="line.1767"></a>
<FONT color="green">1768</FONT>            a = c;<a name="line.1768"></a>
<FONT color="green">1769</FONT>            b = b + d;<a name="line.1769"></a>
<FONT color="green">1770</FONT>    <a name="line.1770"></a>
<FONT color="green">1771</FONT>            t = costA * sinEpsA;<a name="line.1771"></a>
<FONT color="green">1772</FONT>            c = a + t;<a name="line.1772"></a>
<FONT color="green">1773</FONT>            d = -(c - a - t);<a name="line.1773"></a>
<FONT color="green">1774</FONT>            a = c;<a name="line.1774"></a>
<FONT color="green">1775</FONT>            b = b + d;<a name="line.1775"></a>
<FONT color="green">1776</FONT>    <a name="line.1776"></a>
<FONT color="green">1777</FONT>            b = b + sintA * cosEpsB + costA * sinEpsB;<a name="line.1777"></a>
<FONT color="green">1778</FONT>            /*<a name="line.1778"></a>
<FONT color="green">1779</FONT>        t = sintA*cosEpsB;<a name="line.1779"></a>
<FONT color="green">1780</FONT>        c = a + t;<a name="line.1780"></a>
<FONT color="green">1781</FONT>        d = -(c - a - t);<a name="line.1781"></a>
<FONT color="green">1782</FONT>        a = c;<a name="line.1782"></a>
<FONT color="green">1783</FONT>        b = b + d;<a name="line.1783"></a>
<FONT color="green">1784</FONT>    <a name="line.1784"></a>
<FONT color="green">1785</FONT>        t = costA*sinEpsB;<a name="line.1785"></a>
<FONT color="green">1786</FONT>        c = a + t;<a name="line.1786"></a>
<FONT color="green">1787</FONT>        d = -(c - a - t);<a name="line.1787"></a>
<FONT color="green">1788</FONT>        a = c;<a name="line.1788"></a>
<FONT color="green">1789</FONT>        b = b + d;<a name="line.1789"></a>
<FONT color="green">1790</FONT>             */<a name="line.1790"></a>
<FONT color="green">1791</FONT>    <a name="line.1791"></a>
<FONT color="green">1792</FONT>            b = b + sintB + costB * sinEpsA + sintB * cosEpsB + costB * sinEpsB;<a name="line.1792"></a>
<FONT color="green">1793</FONT>            /*<a name="line.1793"></a>
<FONT color="green">1794</FONT>        t = sintB;<a name="line.1794"></a>
<FONT color="green">1795</FONT>        c = a + t;<a name="line.1795"></a>
<FONT color="green">1796</FONT>        d = -(c - a - t);<a name="line.1796"></a>
<FONT color="green">1797</FONT>        a = c;<a name="line.1797"></a>
<FONT color="green">1798</FONT>        b = b + d;<a name="line.1798"></a>
<FONT color="green">1799</FONT>    <a name="line.1799"></a>
<FONT color="green">1800</FONT>        t = costB*sinEpsA;<a name="line.1800"></a>
<FONT color="green">1801</FONT>        c = a + t;<a name="line.1801"></a>
<FONT color="green">1802</FONT>        d = -(c - a - t);<a name="line.1802"></a>
<FONT color="green">1803</FONT>        a = c;<a name="line.1803"></a>
<FONT color="green">1804</FONT>        b = b + d;<a name="line.1804"></a>
<FONT color="green">1805</FONT>    <a name="line.1805"></a>
<FONT color="green">1806</FONT>        t = sintB*cosEpsB;<a name="line.1806"></a>
<FONT color="green">1807</FONT>        c = a + t;<a name="line.1807"></a>
<FONT color="green">1808</FONT>        d = -(c - a - t);<a name="line.1808"></a>
<FONT color="green">1809</FONT>        a = c;<a name="line.1809"></a>
<FONT color="green">1810</FONT>        b = b + d;<a name="line.1810"></a>
<FONT color="green">1811</FONT>    <a name="line.1811"></a>
<FONT color="green">1812</FONT>        t = costB*sinEpsB;<a name="line.1812"></a>
<FONT color="green">1813</FONT>        c = a + t;<a name="line.1813"></a>
<FONT color="green">1814</FONT>        d = -(c - a - t);<a name="line.1814"></a>
<FONT color="green">1815</FONT>        a = c;<a name="line.1815"></a>
<FONT color="green">1816</FONT>        b = b + d;<a name="line.1816"></a>
<FONT color="green">1817</FONT>             */<a name="line.1817"></a>
<FONT color="green">1818</FONT>    <a name="line.1818"></a>
<FONT color="green">1819</FONT>            if (xb != 0.0) {<a name="line.1819"></a>
<FONT color="green">1820</FONT>                t = ((costA + costB) * (cosEpsA + cosEpsB) -<a name="line.1820"></a>
<FONT color="green">1821</FONT>                     (sintA + sintB) * (sinEpsA + sinEpsB)) * xb;  // approximate cosine*xb<a name="line.1821"></a>
<FONT color="green">1822</FONT>                c = a + t;<a name="line.1822"></a>
<FONT color="green">1823</FONT>                d = -(c - a - t);<a name="line.1823"></a>
<FONT color="green">1824</FONT>                a = c;<a name="line.1824"></a>
<FONT color="green">1825</FONT>                b = b + d;<a name="line.1825"></a>
<FONT color="green">1826</FONT>            }<a name="line.1826"></a>
<FONT color="green">1827</FONT>    <a name="line.1827"></a>
<FONT color="green">1828</FONT>            result = a + b;<a name="line.1828"></a>
<FONT color="green">1829</FONT>    <a name="line.1829"></a>
<FONT color="green">1830</FONT>            return result;<a name="line.1830"></a>
<FONT color="green">1831</FONT>        }<a name="line.1831"></a>
<FONT color="green">1832</FONT>    <a name="line.1832"></a>
<FONT color="green">1833</FONT>        /**<a name="line.1833"></a>
<FONT color="green">1834</FONT>         * Compute cosine in the first quadrant by subtracting input from PI/2 and<a name="line.1834"></a>
<FONT color="green">1835</FONT>         * then calling sinQ.  This is more accurate as the input approaches PI/2.<a name="line.1835"></a>
<FONT color="green">1836</FONT>         *  @param xa number from which cosine is requested<a name="line.1836"></a>
<FONT color="green">1837</FONT>         *  @param xb extra bits for x (may be 0.0)<a name="line.1837"></a>
<FONT color="green">1838</FONT>         *  @return cos(xa + xb)<a name="line.1838"></a>
<FONT color="green">1839</FONT>         */<a name="line.1839"></a>
<FONT color="green">1840</FONT>        private static double cosQ(double xa, double xb) {<a name="line.1840"></a>
<FONT color="green">1841</FONT>            final double pi2a = 1.5707963267948966;<a name="line.1841"></a>
<FONT color="green">1842</FONT>            final double pi2b = 6.123233995736766E-17;<a name="line.1842"></a>
<FONT color="green">1843</FONT>    <a name="line.1843"></a>
<FONT color="green">1844</FONT>            final double a = pi2a - xa;<a name="line.1844"></a>
<FONT color="green">1845</FONT>            double b = -(a - pi2a + xa);<a name="line.1845"></a>
<FONT color="green">1846</FONT>            b += pi2b - xb;<a name="line.1846"></a>
<FONT color="green">1847</FONT>    <a name="line.1847"></a>
<FONT color="green">1848</FONT>            return sinQ(a, b);<a name="line.1848"></a>
<FONT color="green">1849</FONT>        }<a name="line.1849"></a>
<FONT color="green">1850</FONT>    <a name="line.1850"></a>
<FONT color="green">1851</FONT>        /**<a name="line.1851"></a>
<FONT color="green">1852</FONT>         *  Compute tangent (or cotangent) over the first quadrant.   0 &lt; x &lt; pi/2<a name="line.1852"></a>
<FONT color="green">1853</FONT>         *  Use combination of table lookup and rational polynomial expansion.<a name="line.1853"></a>
<FONT color="green">1854</FONT>         *  @param xa number from which sine is requested<a name="line.1854"></a>
<FONT color="green">1855</FONT>         *  @param xb extra bits for x (may be 0.0)<a name="line.1855"></a>
<FONT color="green">1856</FONT>         *  @param cotanFlag if true, compute the cotangent instead of the tangent<a name="line.1856"></a>
<FONT color="green">1857</FONT>         *  @return tan(xa+xb) (or cotangent, depending on cotanFlag)<a name="line.1857"></a>
<FONT color="green">1858</FONT>         */<a name="line.1858"></a>
<FONT color="green">1859</FONT>        private static double tanQ(double xa, double xb, boolean cotanFlag) {<a name="line.1859"></a>
<FONT color="green">1860</FONT>    <a name="line.1860"></a>
<FONT color="green">1861</FONT>            int idx = (int) ((xa * 8.0) + 0.5);<a name="line.1861"></a>
<FONT color="green">1862</FONT>            final double epsilon = xa - EIGHTHS[idx]; //idx*0.125;<a name="line.1862"></a>
<FONT color="green">1863</FONT>    <a name="line.1863"></a>
<FONT color="green">1864</FONT>            // Table lookups<a name="line.1864"></a>
<FONT color="green">1865</FONT>            final double sintA = SINE_TABLE_A[idx];<a name="line.1865"></a>
<FONT color="green">1866</FONT>            final double sintB = SINE_TABLE_B[idx];<a name="line.1866"></a>
<FONT color="green">1867</FONT>            final double costA = COSINE_TABLE_A[idx];<a name="line.1867"></a>
<FONT color="green">1868</FONT>            final double costB = COSINE_TABLE_B[idx];<a name="line.1868"></a>
<FONT color="green">1869</FONT>    <a name="line.1869"></a>
<FONT color="green">1870</FONT>            // Polynomial eval of sin(epsilon), cos(epsilon)<a name="line.1870"></a>
<FONT color="green">1871</FONT>            double sinEpsA = epsilon;<a name="line.1871"></a>
<FONT color="green">1872</FONT>            double sinEpsB = polySine(epsilon);<a name="line.1872"></a>
<FONT color="green">1873</FONT>            final double cosEpsA = 1.0;<a name="line.1873"></a>
<FONT color="green">1874</FONT>            final double cosEpsB = polyCosine(epsilon);<a name="line.1874"></a>
<FONT color="green">1875</FONT>    <a name="line.1875"></a>
<FONT color="green">1876</FONT>            // Split epsilon   xa + xb = x<a name="line.1876"></a>
<FONT color="green">1877</FONT>            double temp = sinEpsA * HEX_40000000;<a name="line.1877"></a>
<FONT color="green">1878</FONT>            double temp2 = (sinEpsA + temp) - temp;<a name="line.1878"></a>
<FONT color="green">1879</FONT>            sinEpsB +=  sinEpsA - temp2;<a name="line.1879"></a>
<FONT color="green">1880</FONT>            sinEpsA = temp2;<a name="line.1880"></a>
<FONT color="green">1881</FONT>    <a name="line.1881"></a>
<FONT color="green">1882</FONT>            /* Compute sin(x) by angle addition formula */<a name="line.1882"></a>
<FONT color="green">1883</FONT>    <a name="line.1883"></a>
<FONT color="green">1884</FONT>            /* Compute the following sum:<a name="line.1884"></a>
<FONT color="green">1885</FONT>             *<a name="line.1885"></a>
<FONT color="green">1886</FONT>             * result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +<a name="line.1886"></a>
<FONT color="green">1887</FONT>             *          sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;<a name="line.1887"></a>
<FONT color="green">1888</FONT>             *<a name="line.1888"></a>
<FONT color="green">1889</FONT>             * Ranges of elements<a name="line.1889"></a>
<FONT color="green">1890</FONT>             *<a name="line.1890"></a>
<FONT color="green">1891</FONT>             * xxxtA   0            PI/2<a name="line.1891"></a>
<FONT color="green">1892</FONT>             * xxxtB   -1.5e-9      1.5e-9<a name="line.1892"></a>
<FONT color="green">1893</FONT>             * sinEpsA -0.0625      0.0625<a name="line.1893"></a>
<FONT color="green">1894</FONT>             * sinEpsB -6e-11       6e-11<a name="line.1894"></a>
<FONT color="green">1895</FONT>             * cosEpsA  1.0<a name="line.1895"></a>
<FONT color="green">1896</FONT>             * cosEpsB  0           -0.0625<a name="line.1896"></a>
<FONT color="green">1897</FONT>             *<a name="line.1897"></a>
<FONT color="green">1898</FONT>             */<a name="line.1898"></a>
<FONT color="green">1899</FONT>    <a name="line.1899"></a>
<FONT color="green">1900</FONT>            //result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +<a name="line.1900"></a>
<FONT color="green">1901</FONT>            //          sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;<a name="line.1901"></a>
<FONT color="green">1902</FONT>    <a name="line.1902"></a>
<FONT color="green">1903</FONT>            //result = sintA + sintA*cosEpsB + sintB + sintB * cosEpsB;<a name="line.1903"></a>
<FONT color="green">1904</FONT>            //result += costA*sinEpsA + costA*sinEpsB + costB*sinEpsA + costB * sinEpsB;<a name="line.1904"></a>
<FONT color="green">1905</FONT>            double a = 0;<a name="line.1905"></a>
<FONT color="green">1906</FONT>            double b = 0;<a name="line.1906"></a>
<FONT color="green">1907</FONT>    <a name="line.1907"></a>
<FONT color="green">1908</FONT>            // Compute sine<a name="line.1908"></a>
<FONT color="green">1909</FONT>            double t = sintA;<a name="line.1909"></a>
<FONT color="green">1910</FONT>            double c = a + t;<a name="line.1910"></a>
<FONT color="green">1911</FONT>            double d = -(c - a - t);<a name="line.1911"></a>
<FONT color="green">1912</FONT>            a = c;<a name="line.1912"></a>
<FONT color="green">1913</FONT>            b = b + d;<a name="line.1913"></a>
<FONT color="green">1914</FONT>    <a name="line.1914"></a>
<FONT color="green">1915</FONT>            t = costA*sinEpsA;<a name="line.1915"></a>
<FONT color="green">1916</FONT>            c = a + t;<a name="line.1916"></a>
<FONT color="green">1917</FONT>            d = -(c - a - t);<a name="line.1917"></a>
<FONT color="green">1918</FONT>            a = c;<a name="line.1918"></a>
<FONT color="green">1919</FONT>            b = b + d;<a name="line.1919"></a>
<FONT color="green">1920</FONT>    <a name="line.1920"></a>
<FONT color="green">1921</FONT>            b = b + sintA*cosEpsB + costA*sinEpsB;<a name="line.1921"></a>
<FONT color="green">1922</FONT>            b = b + sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;<a name="line.1922"></a>
<FONT color="green">1923</FONT>    <a name="line.1923"></a>
<FONT color="green">1924</FONT>            double sina = a + b;<a name="line.1924"></a>
<FONT color="green">1925</FONT>            double sinb = -(sina - a - b);<a name="line.1925"></a>
<FONT color="green">1926</FONT>    <a name="line.1926"></a>
<FONT color="green">1927</FONT>            // Compute cosine<a name="line.1927"></a>
<FONT color="green">1928</FONT>    <a name="line.1928"></a>
<FONT color="green">1929</FONT>            a = b = c = d = 0.0;<a name="line.1929"></a>
<FONT color="green">1930</FONT>    <a name="line.1930"></a>
<FONT color="green">1931</FONT>            t = costA*cosEpsA;<a name="line.1931"></a>
<FONT color="green">1932</FONT>            c = a + t;<a name="line.1932"></a>
<FONT color="green">1933</FONT>            d = -(c - a - t);<a name="line.1933"></a>
<FONT color="green">1934</FONT>            a = c;<a name="line.1934"></a>
<FONT color="green">1935</FONT>            b = b + d;<a name="line.1935"></a>
<FONT color="green">1936</FONT>    <a name="line.1936"></a>
<FONT color="green">1937</FONT>            t = -sintA*sinEpsA;<a name="line.1937"></a>
<FONT color="green">1938</FONT>            c = a + t;<a name="line.1938"></a>
<FONT color="green">1939</FONT>            d = -(c - a - t);<a name="line.1939"></a>
<FONT color="green">1940</FONT>            a = c;<a name="line.1940"></a>
<FONT color="green">1941</FONT>            b = b + d;<a name="line.1941"></a>
<FONT color="green">1942</FONT>    <a name="line.1942"></a>
<FONT color="green">1943</FONT>            b = b + costB*cosEpsA + costA*cosEpsB + costB*cosEpsB;<a name="line.1943"></a>
<FONT color="green">1944</FONT>            b = b - (sintB*sinEpsA + sintA*sinEpsB + sintB*sinEpsB);<a name="line.1944"></a>
<FONT color="green">1945</FONT>    <a name="line.1945"></a>
<FONT color="green">1946</FONT>            double cosa = a + b;<a name="line.1946"></a>
<FONT color="green">1947</FONT>            double cosb = -(cosa - a - b);<a name="line.1947"></a>
<FONT color="green">1948</FONT>    <a name="line.1948"></a>
<FONT color="green">1949</FONT>            if (cotanFlag) {<a name="line.1949"></a>
<FONT color="green">1950</FONT>                double tmp;<a name="line.1950"></a>
<FONT color="green">1951</FONT>                tmp = cosa; cosa = sina; sina = tmp;<a name="line.1951"></a>
<FONT color="green">1952</FONT>                tmp = cosb; cosb = sinb; sinb = tmp;<a name="line.1952"></a>
<FONT color="green">1953</FONT>            }<a name="line.1953"></a>
<FONT color="green">1954</FONT>    <a name="line.1954"></a>
<FONT color="green">1955</FONT>    <a name="line.1955"></a>
<FONT color="green">1956</FONT>            /* estimate and correct, compute 1.0/(cosa+cosb) */<a name="line.1956"></a>
<FONT color="green">1957</FONT>            /*<a name="line.1957"></a>
<FONT color="green">1958</FONT>        double est = (sina+sinb)/(cosa+cosb);<a name="line.1958"></a>
<FONT color="green">1959</FONT>        double err = (sina - cosa*est) + (sinb - cosb*est);<a name="line.1959"></a>
<FONT color="green">1960</FONT>        est += err/(cosa+cosb);<a name="line.1960"></a>
<FONT color="green">1961</FONT>        err = (sina - cosa*est) + (sinb - cosb*est);<a name="line.1961"></a>
<FONT color="green">1962</FONT>             */<a name="line.1962"></a>
<FONT color="green">1963</FONT>    <a name="line.1963"></a>
<FONT color="green">1964</FONT>            // f(x) = 1/x,   f'(x) = -1/x^2<a name="line.1964"></a>
<FONT color="green">1965</FONT>    <a name="line.1965"></a>
<FONT color="green">1966</FONT>            double est = sina/cosa;<a name="line.1966"></a>
<FONT color="green">1967</FONT>    <a name="line.1967"></a>
<FONT color="green">1968</FONT>            /* Split the estimate to get more accurate read on division rounding */<a name="line.1968"></a>
<FONT color="green">1969</FONT>            temp = est * HEX_40000000;<a name="line.1969"></a>
<FONT color="green">1970</FONT>            double esta = (est + temp) - temp;<a name="line.1970"></a>
<FONT color="green">1971</FONT>            double estb =  est - esta;<a name="line.1971"></a>
<FONT color="green">1972</FONT>    <a name="line.1972"></a>
<FONT color="green">1973</FONT>            temp = cosa * HEX_40000000;<a name="line.1973"></a>
<FONT color="green">1974</FONT>            double cosaa = (cosa + temp) - temp;<a name="line.1974"></a>
<FONT color="green">1975</FONT>            double cosab =  cosa - cosaa;<a name="line.1975"></a>
<FONT color="green">1976</FONT>    <a name="line.1976"></a>
<FONT color="green">1977</FONT>            //double err = (sina - est*cosa)/cosa;  // Correction for division rounding<a name="line.1977"></a>
<FONT color="green">1978</FONT>            double err = (sina - esta*cosaa - esta*cosab - estb*cosaa - estb*cosab)/cosa;  // Correction for division rounding<a name="line.1978"></a>
<FONT color="green">1979</FONT>            err += sinb/cosa;                     // Change in est due to sinb<a name="line.1979"></a>
<FONT color="green">1980</FONT>            err += -sina * cosb / cosa / cosa;    // Change in est due to cosb<a name="line.1980"></a>
<FONT color="green">1981</FONT>    <a name="line.1981"></a>
<FONT color="green">1982</FONT>            if (xb != 0.0) {<a name="line.1982"></a>
<FONT color="green">1983</FONT>                // tan' = 1 + tan^2      cot' = -(1 + cot^2)<a name="line.1983"></a>
<FONT color="green">1984</FONT>                // Approximate impact of xb<a name="line.1984"></a>
<FONT color="green">1985</FONT>                double xbadj = xb + est*est*xb;<a name="line.1985"></a>
<FONT color="green">1986</FONT>                if (cotanFlag) {<a name="line.1986"></a>
<FONT color="green">1987</FONT>                    xbadj = -xbadj;<a name="line.1987"></a>
<FONT color="green">1988</FONT>                }<a name="line.1988"></a>
<FONT color="green">1989</FONT>    <a name="line.1989"></a>
<FONT color="green">1990</FONT>                err += xbadj;<a name="line.1990"></a>
<FONT color="green">1991</FONT>            }<a name="line.1991"></a>
<FONT color="green">1992</FONT>    <a name="line.1992"></a>
<FONT color="green">1993</FONT>            return est+err;<a name="line.1993"></a>
<FONT color="green">1994</FONT>        }<a name="line.1994"></a>
<FONT color="green">1995</FONT>    <a name="line.1995"></a>
<FONT color="green">1996</FONT>        /** Reduce the input argument using the Payne and Hanek method.<a name="line.1996"></a>
<FONT color="green">1997</FONT>         *  This is good for all inputs 0.0 &lt; x &lt; inf<a name="line.1997"></a>
<FONT color="green">1998</FONT>         *  Output is remainder after dividing by PI/2<a name="line.1998"></a>
<FONT color="green">1999</FONT>         *  The result array should contain 3 numbers.<a name="line.1999"></a>
<FONT color="green">2000</FONT>         *  result[0] is the integer portion, so mod 4 this gives the quadrant.<a name="line.2000"></a>
<FONT color="green">2001</FONT>         *  result[1] is the upper bits of the remainder<a name="line.2001"></a>
<FONT color="green">2002</FONT>         *  result[2] is the lower bits of the remainder<a name="line.2002"></a>
<FONT color="green">2003</FONT>         *<a name="line.2003"></a>
<FONT color="green">2004</FONT>         * @param x number to reduce<a name="line.2004"></a>
<FONT color="green">2005</FONT>         * @param result placeholder where to put the result<a name="line.2005"></a>
<FONT color="green">2006</FONT>         */<a name="line.2006"></a>
<FONT color="green">2007</FONT>        private static void reducePayneHanek(double x, double result[])<a name="line.2007"></a>
<FONT color="green">2008</FONT>        {<a name="line.2008"></a>
<FONT color="green">2009</FONT>            /* Convert input double to bits */<a name="line.2009"></a>
<FONT color="green">2010</FONT>            long inbits = Double.doubleToLongBits(x);<a name="line.2010"></a>
<FONT color="green">2011</FONT>            int exponent = (int) ((inbits &gt;&gt; 52) &amp; 0x7ff) - 1023;<a name="line.2011"></a>
<FONT color="green">2012</FONT>    <a name="line.2012"></a>
<FONT color="green">2013</FONT>            /* Convert to fixed point representation */<a name="line.2013"></a>
<FONT color="green">2014</FONT>            inbits &amp;= 0x000fffffffffffffL;<a name="line.2014"></a>
<FONT color="green">2015</FONT>            inbits |= 0x0010000000000000L;<a name="line.2015"></a>
<FONT color="green">2016</FONT>    <a name="line.2016"></a>
<FONT color="green">2017</FONT>            /* Normalize input to be between 0.5 and 1.0 */<a name="line.2017"></a>
<FONT color="green">2018</FONT>            exponent++;<a name="line.2018"></a>
<FONT color="green">2019</FONT>            inbits &lt;&lt;= 11;<a name="line.2019"></a>
<FONT color="green">2020</FONT>    <a name="line.2020"></a>
<FONT color="green">2021</FONT>            /* Based on the exponent, get a shifted copy of recip2pi */<a name="line.2021"></a>
<FONT color="green">2022</FONT>            long shpi0;<a name="line.2022"></a>
<FONT color="green">2023</FONT>            long shpiA;<a name="line.2023"></a>
<FONT color="green">2024</FONT>            long shpiB;<a name="line.2024"></a>
<FONT color="green">2025</FONT>            int idx = exponent &gt;&gt; 6;<a name="line.2025"></a>
<FONT color="green">2026</FONT>            int shift = exponent - (idx &lt;&lt; 6);<a name="line.2026"></a>
<FONT color="green">2027</FONT>    <a name="line.2027"></a>
<FONT color="green">2028</FONT>            if (shift != 0) {<a name="line.2028"></a>
<FONT color="green">2029</FONT>                shpi0 = (idx == 0) ? 0 : (RECIP_2PI[idx-1] &lt;&lt; shift);<a name="line.2029"></a>
<FONT color="green">2030</FONT>                shpi0 |= RECIP_2PI[idx] &gt;&gt;&gt; (64-shift);<a name="line.2030"></a>
<FONT color="green">2031</FONT>                shpiA = (RECIP_2PI[idx] &lt;&lt; shift) | (RECIP_2PI[idx+1] &gt;&gt;&gt; (64-shift));<a name="line.2031"></a>
<FONT color="green">2032</FONT>                shpiB = (RECIP_2PI[idx+1] &lt;&lt; shift) | (RECIP_2PI[idx+2] &gt;&gt;&gt; (64-shift));<a name="line.2032"></a>
<FONT color="green">2033</FONT>            } else {<a name="line.2033"></a>
<FONT color="green">2034</FONT>                shpi0 = (idx == 0) ? 0 : RECIP_2PI[idx-1];<a name="line.2034"></a>
<FONT color="green">2035</FONT>                shpiA = RECIP_2PI[idx];<a name="line.2035"></a>
<FONT color="green">2036</FONT>                shpiB = RECIP_2PI[idx+1];<a name="line.2036"></a>
<FONT color="green">2037</FONT>            }<a name="line.2037"></a>
<FONT color="green">2038</FONT>    <a name="line.2038"></a>
<FONT color="green">2039</FONT>            /* Multiply input by shpiA */<a name="line.2039"></a>
<FONT color="green">2040</FONT>            long a = inbits &gt;&gt;&gt; 32;<a name="line.2040"></a>
<FONT color="green">2041</FONT>            long b = inbits &amp; 0xffffffffL;<a name="line.2041"></a>
<FONT color="green">2042</FONT>    <a name="line.2042"></a>
<FONT color="green">2043</FONT>            long c = shpiA &gt;&gt;&gt; 32;<a name="line.2043"></a>
<FONT color="green">2044</FONT>            long d = shpiA &amp; 0xffffffffL;<a name="line.2044"></a>
<FONT color="green">2045</FONT>    <a name="line.2045"></a>
<FONT color="green">2046</FONT>            long ac = a * c;<a name="line.2046"></a>
<FONT color="green">2047</FONT>            long bd = b * d;<a name="line.2047"></a>
<FONT color="green">2048</FONT>            long bc = b * c;<a name="line.2048"></a>
<FONT color="green">2049</FONT>            long ad = a * d;<a name="line.2049"></a>
<FONT color="green">2050</FONT>    <a name="line.2050"></a>
<FONT color="green">2051</FONT>            long prodB = bd + (ad &lt;&lt; 32);<a name="line.2051"></a>
<FONT color="green">2052</FONT>            long prodA = ac + (ad &gt;&gt;&gt; 32);<a name="line.2052"></a>
<FONT color="green">2053</FONT>    <a name="line.2053"></a>
<FONT color="green">2054</FONT>            boolean bita = (bd &amp; 0x8000000000000000L) != 0;<a name="line.2054"></a>
<FONT color="green">2055</FONT>            boolean bitb = (ad &amp; 0x80000000L ) != 0;<a name="line.2055"></a>
<FONT color="green">2056</FONT>            boolean bitsum = (prodB &amp; 0x8000000000000000L) != 0;<a name="line.2056"></a>
<FONT color="green">2057</FONT>    <a name="line.2057"></a>
<FONT color="green">2058</FONT>            /* Carry */<a name="line.2058"></a>
<FONT color="green">2059</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2059"></a>
<FONT color="green">2060</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2060"></a>
<FONT color="green">2061</FONT>                prodA++;<a name="line.2061"></a>
<FONT color="green">2062</FONT>            }<a name="line.2062"></a>
<FONT color="green">2063</FONT>    <a name="line.2063"></a>
<FONT color="green">2064</FONT>            bita = (prodB &amp; 0x8000000000000000L) != 0;<a name="line.2064"></a>
<FONT color="green">2065</FONT>            bitb = (bc &amp; 0x80000000L ) != 0;<a name="line.2065"></a>
<FONT color="green">2066</FONT>    <a name="line.2066"></a>
<FONT color="green">2067</FONT>            prodB = prodB + (bc &lt;&lt; 32);<a name="line.2067"></a>
<FONT color="green">2068</FONT>            prodA = prodA + (bc &gt;&gt;&gt; 32);<a name="line.2068"></a>
<FONT color="green">2069</FONT>    <a name="line.2069"></a>
<FONT color="green">2070</FONT>            bitsum = (prodB &amp; 0x8000000000000000L) != 0;<a name="line.2070"></a>
<FONT color="green">2071</FONT>    <a name="line.2071"></a>
<FONT color="green">2072</FONT>            /* Carry */<a name="line.2072"></a>
<FONT color="green">2073</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2073"></a>
<FONT color="green">2074</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2074"></a>
<FONT color="green">2075</FONT>                prodA++;<a name="line.2075"></a>
<FONT color="green">2076</FONT>            }<a name="line.2076"></a>
<FONT color="green">2077</FONT>    <a name="line.2077"></a>
<FONT color="green">2078</FONT>            /* Multiply input by shpiB */<a name="line.2078"></a>
<FONT color="green">2079</FONT>            c = shpiB &gt;&gt;&gt; 32;<a name="line.2079"></a>
<FONT color="green">2080</FONT>            d = shpiB &amp; 0xffffffffL;<a name="line.2080"></a>
<FONT color="green">2081</FONT>            ac = a * c;<a name="line.2081"></a>
<FONT color="green">2082</FONT>            bc = b * c;<a name="line.2082"></a>
<FONT color="green">2083</FONT>            ad = a * d;<a name="line.2083"></a>
<FONT color="green">2084</FONT>    <a name="line.2084"></a>
<FONT color="green">2085</FONT>            /* Collect terms */<a name="line.2085"></a>
<FONT color="green">2086</FONT>            ac = ac + ((bc + ad) &gt;&gt;&gt; 32);<a name="line.2086"></a>
<FONT color="green">2087</FONT>    <a name="line.2087"></a>
<FONT color="green">2088</FONT>            bita = (prodB &amp; 0x8000000000000000L) != 0;<a name="line.2088"></a>
<FONT color="green">2089</FONT>            bitb = (ac &amp; 0x8000000000000000L ) != 0;<a name="line.2089"></a>
<FONT color="green">2090</FONT>            prodB += ac;<a name="line.2090"></a>
<FONT color="green">2091</FONT>            bitsum = (prodB &amp; 0x8000000000000000L) != 0;<a name="line.2091"></a>
<FONT color="green">2092</FONT>            /* Carry */<a name="line.2092"></a>
<FONT color="green">2093</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2093"></a>
<FONT color="green">2094</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2094"></a>
<FONT color="green">2095</FONT>                prodA++;<a name="line.2095"></a>
<FONT color="green">2096</FONT>            }<a name="line.2096"></a>
<FONT color="green">2097</FONT>    <a name="line.2097"></a>
<FONT color="green">2098</FONT>            /* Multiply by shpi0 */<a name="line.2098"></a>
<FONT color="green">2099</FONT>            c = shpi0 &gt;&gt;&gt; 32;<a name="line.2099"></a>
<FONT color="green">2100</FONT>            d = shpi0 &amp; 0xffffffffL;<a name="line.2100"></a>
<FONT color="green">2101</FONT>    <a name="line.2101"></a>
<FONT color="green">2102</FONT>            bd = b * d;<a name="line.2102"></a>
<FONT color="green">2103</FONT>            bc = b * c;<a name="line.2103"></a>
<FONT color="green">2104</FONT>            ad = a * d;<a name="line.2104"></a>
<FONT color="green">2105</FONT>    <a name="line.2105"></a>
<FONT color="green">2106</FONT>            prodA += bd + ((bc + ad) &lt;&lt; 32);<a name="line.2106"></a>
<FONT color="green">2107</FONT>    <a name="line.2107"></a>
<FONT color="green">2108</FONT>            /*<a name="line.2108"></a>
<FONT color="green">2109</FONT>             * prodA, prodB now contain the remainder as a fraction of PI.  We want this as a fraction of<a name="line.2109"></a>
<FONT color="green">2110</FONT>             * PI/2, so use the following steps:<a name="line.2110"></a>
<FONT color="green">2111</FONT>             * 1.) multiply by 4.<a name="line.2111"></a>
<FONT color="green">2112</FONT>             * 2.) do a fixed point muliply by PI/4.<a name="line.2112"></a>
<FONT color="green">2113</FONT>             * 3.) Convert to floating point.<a name="line.2113"></a>
<FONT color="green">2114</FONT>             * 4.) Multiply by 2<a name="line.2114"></a>
<FONT color="green">2115</FONT>             */<a name="line.2115"></a>
<FONT color="green">2116</FONT>    <a name="line.2116"></a>
<FONT color="green">2117</FONT>            /* This identifies the quadrant */<a name="line.2117"></a>
<FONT color="green">2118</FONT>            int intPart = (int)(prodA &gt;&gt;&gt; 62);<a name="line.2118"></a>
<FONT color="green">2119</FONT>    <a name="line.2119"></a>
<FONT color="green">2120</FONT>            /* Multiply by 4 */<a name="line.2120"></a>
<FONT color="green">2121</FONT>            prodA &lt;&lt;= 2;<a name="line.2121"></a>
<FONT color="green">2122</FONT>            prodA |= prodB &gt;&gt;&gt; 62;<a name="line.2122"></a>
<FONT color="green">2123</FONT>            prodB &lt;&lt;= 2;<a name="line.2123"></a>
<FONT color="green">2124</FONT>    <a name="line.2124"></a>
<FONT color="green">2125</FONT>            /* Multiply by PI/4 */<a name="line.2125"></a>
<FONT color="green">2126</FONT>            a = prodA &gt;&gt;&gt; 32;<a name="line.2126"></a>
<FONT color="green">2127</FONT>            b = prodA &amp; 0xffffffffL;<a name="line.2127"></a>
<FONT color="green">2128</FONT>    <a name="line.2128"></a>
<FONT color="green">2129</FONT>            c = PI_O_4_BITS[0] &gt;&gt;&gt; 32;<a name="line.2129"></a>
<FONT color="green">2130</FONT>            d = PI_O_4_BITS[0] &amp; 0xffffffffL;<a name="line.2130"></a>
<FONT color="green">2131</FONT>    <a name="line.2131"></a>
<FONT color="green">2132</FONT>            ac = a * c;<a name="line.2132"></a>
<FONT color="green">2133</FONT>            bd = b * d;<a name="line.2133"></a>
<FONT color="green">2134</FONT>            bc = b * c;<a name="line.2134"></a>
<FONT color="green">2135</FONT>            ad = a * d;<a name="line.2135"></a>
<FONT color="green">2136</FONT>    <a name="line.2136"></a>
<FONT color="green">2137</FONT>            long prod2B = bd + (ad &lt;&lt; 32);<a name="line.2137"></a>
<FONT color="green">2138</FONT>            long prod2A = ac + (ad &gt;&gt;&gt; 32);<a name="line.2138"></a>
<FONT color="green">2139</FONT>    <a name="line.2139"></a>
<FONT color="green">2140</FONT>            bita = (bd &amp; 0x8000000000000000L) != 0;<a name="line.2140"></a>
<FONT color="green">2141</FONT>            bitb = (ad &amp; 0x80000000L ) != 0;<a name="line.2141"></a>
<FONT color="green">2142</FONT>            bitsum = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2142"></a>
<FONT color="green">2143</FONT>    <a name="line.2143"></a>
<FONT color="green">2144</FONT>            /* Carry */<a name="line.2144"></a>
<FONT color="green">2145</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2145"></a>
<FONT color="green">2146</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2146"></a>
<FONT color="green">2147</FONT>                prod2A++;<a name="line.2147"></a>
<FONT color="green">2148</FONT>            }<a name="line.2148"></a>
<FONT color="green">2149</FONT>    <a name="line.2149"></a>
<FONT color="green">2150</FONT>            bita = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2150"></a>
<FONT color="green">2151</FONT>            bitb = (bc &amp; 0x80000000L ) != 0;<a name="line.2151"></a>
<FONT color="green">2152</FONT>    <a name="line.2152"></a>
<FONT color="green">2153</FONT>            prod2B = prod2B + (bc &lt;&lt; 32);<a name="line.2153"></a>
<FONT color="green">2154</FONT>            prod2A = prod2A + (bc &gt;&gt;&gt; 32);<a name="line.2154"></a>
<FONT color="green">2155</FONT>    <a name="line.2155"></a>
<FONT color="green">2156</FONT>            bitsum = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2156"></a>
<FONT color="green">2157</FONT>    <a name="line.2157"></a>
<FONT color="green">2158</FONT>            /* Carry */<a name="line.2158"></a>
<FONT color="green">2159</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2159"></a>
<FONT color="green">2160</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2160"></a>
<FONT color="green">2161</FONT>                prod2A++;<a name="line.2161"></a>
<FONT color="green">2162</FONT>            }<a name="line.2162"></a>
<FONT color="green">2163</FONT>    <a name="line.2163"></a>
<FONT color="green">2164</FONT>            /* Multiply input by pio4bits[1] */<a name="line.2164"></a>
<FONT color="green">2165</FONT>            c = PI_O_4_BITS[1] &gt;&gt;&gt; 32;<a name="line.2165"></a>
<FONT color="green">2166</FONT>            d = PI_O_4_BITS[1] &amp; 0xffffffffL;<a name="line.2166"></a>
<FONT color="green">2167</FONT>            ac = a * c;<a name="line.2167"></a>
<FONT color="green">2168</FONT>            bc = b * c;<a name="line.2168"></a>
<FONT color="green">2169</FONT>            ad = a * d;<a name="line.2169"></a>
<FONT color="green">2170</FONT>    <a name="line.2170"></a>
<FONT color="green">2171</FONT>            /* Collect terms */<a name="line.2171"></a>
<FONT color="green">2172</FONT>            ac = ac + ((bc + ad) &gt;&gt;&gt; 32);<a name="line.2172"></a>
<FONT color="green">2173</FONT>    <a name="line.2173"></a>
<FONT color="green">2174</FONT>            bita = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2174"></a>
<FONT color="green">2175</FONT>            bitb = (ac &amp; 0x8000000000000000L ) != 0;<a name="line.2175"></a>
<FONT color="green">2176</FONT>            prod2B += ac;<a name="line.2176"></a>
<FONT color="green">2177</FONT>            bitsum = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2177"></a>
<FONT color="green">2178</FONT>            /* Carry */<a name="line.2178"></a>
<FONT color="green">2179</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2179"></a>
<FONT color="green">2180</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2180"></a>
<FONT color="green">2181</FONT>                prod2A++;<a name="line.2181"></a>
<FONT color="green">2182</FONT>            }<a name="line.2182"></a>
<FONT color="green">2183</FONT>    <a name="line.2183"></a>
<FONT color="green">2184</FONT>            /* Multiply inputB by pio4bits[0] */<a name="line.2184"></a>
<FONT color="green">2185</FONT>            a = prodB &gt;&gt;&gt; 32;<a name="line.2185"></a>
<FONT color="green">2186</FONT>            b = prodB &amp; 0xffffffffL;<a name="line.2186"></a>
<FONT color="green">2187</FONT>            c = PI_O_4_BITS[0] &gt;&gt;&gt; 32;<a name="line.2187"></a>
<FONT color="green">2188</FONT>            d = PI_O_4_BITS[0] &amp; 0xffffffffL;<a name="line.2188"></a>
<FONT color="green">2189</FONT>            ac = a * c;<a name="line.2189"></a>
<FONT color="green">2190</FONT>            bc = b * c;<a name="line.2190"></a>
<FONT color="green">2191</FONT>            ad = a * d;<a name="line.2191"></a>
<FONT color="green">2192</FONT>    <a name="line.2192"></a>
<FONT color="green">2193</FONT>            /* Collect terms */<a name="line.2193"></a>
<FONT color="green">2194</FONT>            ac = ac + ((bc + ad) &gt;&gt;&gt; 32);<a name="line.2194"></a>
<FONT color="green">2195</FONT>    <a name="line.2195"></a>
<FONT color="green">2196</FONT>            bita = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2196"></a>
<FONT color="green">2197</FONT>            bitb = (ac &amp; 0x8000000000000000L ) != 0;<a name="line.2197"></a>
<FONT color="green">2198</FONT>            prod2B += ac;<a name="line.2198"></a>
<FONT color="green">2199</FONT>            bitsum = (prod2B &amp; 0x8000000000000000L) != 0;<a name="line.2199"></a>
<FONT color="green">2200</FONT>            /* Carry */<a name="line.2200"></a>
<FONT color="green">2201</FONT>            if ( (bita &amp;&amp; bitb) ||<a name="line.2201"></a>
<FONT color="green">2202</FONT>                    ((bita || bitb) &amp;&amp; !bitsum) ) {<a name="line.2202"></a>
<FONT color="green">2203</FONT>                prod2A++;<a name="line.2203"></a>
<FONT color="green">2204</FONT>            }<a name="line.2204"></a>
<FONT color="green">2205</FONT>    <a name="line.2205"></a>
<FONT color="green">2206</FONT>            /* Convert to double */<a name="line.2206"></a>
<FONT color="green">2207</FONT>            double tmpA = (prod2A &gt;&gt;&gt; 12) / TWO_POWER_52;  // High order 52 bits<a name="line.2207"></a>
<FONT color="green">2208</FONT>            double tmpB = (((prod2A &amp; 0xfffL) &lt;&lt; 40) + (prod2B &gt;&gt;&gt; 24)) / TWO_POWER_52 / TWO_POWER_52; // Low bits<a name="line.2208"></a>
<FONT color="green">2209</FONT>    <a name="line.2209"></a>
<FONT color="green">2210</FONT>            double sumA = tmpA + tmpB;<a name="line.2210"></a>
<FONT color="green">2211</FONT>            double sumB = -(sumA - tmpA - tmpB);<a name="line.2211"></a>
<FONT color="green">2212</FONT>    <a name="line.2212"></a>
<FONT color="green">2213</FONT>            /* Multiply by PI/2 and return */<a name="line.2213"></a>
<FONT color="green">2214</FONT>            result[0] = intPart;<a name="line.2214"></a>
<FONT color="green">2215</FONT>            result[1] = sumA * 2.0;<a name="line.2215"></a>
<FONT color="green">2216</FONT>            result[2] = sumB * 2.0;<a name="line.2216"></a>
<FONT color="green">2217</FONT>        }<a name="line.2217"></a>
<FONT color="green">2218</FONT>    <a name="line.2218"></a>
<FONT color="green">2219</FONT>        /**<a name="line.2219"></a>
<FONT color="green">2220</FONT>         * Sine function.<a name="line.2220"></a>
<FONT color="green">2221</FONT>         *<a name="line.2221"></a>
<FONT color="green">2222</FONT>         * @param x Argument.<a name="line.2222"></a>
<FONT color="green">2223</FONT>         * @return sin(x)<a name="line.2223"></a>
<FONT color="green">2224</FONT>         */<a name="line.2224"></a>
<FONT color="green">2225</FONT>        public static double sin(double x) {<a name="line.2225"></a>
<FONT color="green">2226</FONT>            boolean negative = false;<a name="line.2226"></a>
<FONT color="green">2227</FONT>            int quadrant = 0;<a name="line.2227"></a>
<FONT color="green">2228</FONT>            double xa;<a name="line.2228"></a>
<FONT color="green">2229</FONT>            double xb = 0.0;<a name="line.2229"></a>
<FONT color="green">2230</FONT>    <a name="line.2230"></a>
<FONT color="green">2231</FONT>            /* Take absolute value of the input */<a name="line.2231"></a>
<FONT color="green">2232</FONT>            xa = x;<a name="line.2232"></a>
<FONT color="green">2233</FONT>            if (x &lt; 0) {<a name="line.2233"></a>
<FONT color="green">2234</FONT>                negative = true;<a name="line.2234"></a>
<FONT color="green">2235</FONT>                xa = -xa;<a name="line.2235"></a>
<FONT color="green">2236</FONT>            }<a name="line.2236"></a>
<FONT color="green">2237</FONT>    <a name="line.2237"></a>
<FONT color="green">2238</FONT>            /* Check for zero and negative zero */<a name="line.2238"></a>
<FONT color="green">2239</FONT>            if (xa == 0.0) {<a name="line.2239"></a>
<FONT color="green">2240</FONT>                long bits = Double.doubleToLongBits(x);<a name="line.2240"></a>
<FONT color="green">2241</FONT>                if (bits &lt; 0) {<a name="line.2241"></a>
<FONT color="green">2242</FONT>                    return -0.0;<a name="line.2242"></a>
<FONT color="green">2243</FONT>                }<a name="line.2243"></a>
<FONT color="green">2244</FONT>                return 0.0;<a name="line.2244"></a>
<FONT color="green">2245</FONT>            }<a name="line.2245"></a>
<FONT color="green">2246</FONT>    <a name="line.2246"></a>
<FONT color="green">2247</FONT>            if (xa != xa || xa == Double.POSITIVE_INFINITY) {<a name="line.2247"></a>
<FONT color="green">2248</FONT>                return Double.NaN;<a name="line.2248"></a>
<FONT color="green">2249</FONT>            }<a name="line.2249"></a>
<FONT color="green">2250</FONT>    <a name="line.2250"></a>
<FONT color="green">2251</FONT>            /* Perform any argument reduction */<a name="line.2251"></a>
<FONT color="green">2252</FONT>            if (xa &gt; 3294198.0) {<a name="line.2252"></a>
<FONT color="green">2253</FONT>                // PI * (2**20)<a name="line.2253"></a>
<FONT color="green">2254</FONT>                // Argument too big for CodyWaite reduction.  Must use<a name="line.2254"></a>
<FONT color="green">2255</FONT>                // PayneHanek.<a name="line.2255"></a>
<FONT color="green">2256</FONT>                double reduceResults[] = new double[3];<a name="line.2256"></a>
<FONT color="green">2257</FONT>                reducePayneHanek(xa, reduceResults);<a name="line.2257"></a>
<FONT color="green">2258</FONT>                quadrant = ((int) reduceResults[0]) &amp; 3;<a name="line.2258"></a>
<FONT color="green">2259</FONT>                xa = reduceResults[1];<a name="line.2259"></a>
<FONT color="green">2260</FONT>                xb = reduceResults[2];<a name="line.2260"></a>
<FONT color="green">2261</FONT>            } else if (xa &gt; 1.5707963267948966) {<a name="line.2261"></a>
<FONT color="green">2262</FONT>                final CodyWaite cw = new CodyWaite(xa);<a name="line.2262"></a>
<FONT color="green">2263</FONT>                quadrant = cw.getK() &amp; 3;<a name="line.2263"></a>
<FONT color="green">2264</FONT>                xa = cw.getRemA();<a name="line.2264"></a>
<FONT color="green">2265</FONT>                xb = cw.getRemB();<a name="line.2265"></a>
<FONT color="green">2266</FONT>            }<a name="line.2266"></a>
<FONT color="green">2267</FONT>    <a name="line.2267"></a>
<FONT color="green">2268</FONT>            if (negative) {<a name="line.2268"></a>
<FONT color="green">2269</FONT>                quadrant ^= 2;  // Flip bit 1<a name="line.2269"></a>
<FONT color="green">2270</FONT>            }<a name="line.2270"></a>
<FONT color="green">2271</FONT>    <a name="line.2271"></a>
<FONT color="green">2272</FONT>            switch (quadrant) {<a name="line.2272"></a>
<FONT color="green">2273</FONT>                case 0:<a name="line.2273"></a>
<FONT color="green">2274</FONT>                    return sinQ(xa, xb);<a name="line.2274"></a>
<FONT color="green">2275</FONT>                case 1:<a name="line.2275"></a>
<FONT color="green">2276</FONT>                    return cosQ(xa, xb);<a name="line.2276"></a>
<FONT color="green">2277</FONT>                case 2:<a name="line.2277"></a>
<FONT color="green">2278</FONT>                    return -sinQ(xa, xb);<a name="line.2278"></a>
<FONT color="green">2279</FONT>                case 3:<a name="line.2279"></a>
<FONT color="green">2280</FONT>                    return -cosQ(xa, xb);<a name="line.2280"></a>
<FONT color="green">2281</FONT>                default:<a name="line.2281"></a>
<FONT color="green">2282</FONT>                    return Double.NaN;<a name="line.2282"></a>
<FONT color="green">2283</FONT>            }<a name="line.2283"></a>
<FONT color="green">2284</FONT>        }<a name="line.2284"></a>
<FONT color="green">2285</FONT>    <a name="line.2285"></a>
<FONT color="green">2286</FONT>        /**<a name="line.2286"></a>
<FONT color="green">2287</FONT>         * Cosine function.<a name="line.2287"></a>
<FONT color="green">2288</FONT>         *<a name="line.2288"></a>
<FONT color="green">2289</FONT>         * @param x Argument.<a name="line.2289"></a>
<FONT color="green">2290</FONT>         * @return cos(x)<a name="line.2290"></a>
<FONT color="green">2291</FONT>         */<a name="line.2291"></a>
<FONT color="green">2292</FONT>        public static double cos(double x) {<a name="line.2292"></a>
<FONT color="green">2293</FONT>            int quadrant = 0;<a name="line.2293"></a>
<FONT color="green">2294</FONT>    <a name="line.2294"></a>
<FONT color="green">2295</FONT>            /* Take absolute value of the input */<a name="line.2295"></a>
<FONT color="green">2296</FONT>            double xa = x;<a name="line.2296"></a>
<FONT color="green">2297</FONT>            if (x &lt; 0) {<a name="line.2297"></a>
<FONT color="green">2298</FONT>                xa = -xa;<a name="line.2298"></a>
<FONT color="green">2299</FONT>            }<a name="line.2299"></a>
<FONT color="green">2300</FONT>    <a name="line.2300"></a>
<FONT color="green">2301</FONT>            if (xa != xa || xa == Double.POSITIVE_INFINITY) {<a name="line.2301"></a>
<FONT color="green">2302</FONT>                return Double.NaN;<a name="line.2302"></a>
<FONT color="green">2303</FONT>            }<a name="line.2303"></a>
<FONT color="green">2304</FONT>    <a name="line.2304"></a>
<FONT color="green">2305</FONT>            /* Perform any argument reduction */<a name="line.2305"></a>
<FONT color="green">2306</FONT>            double xb = 0;<a name="line.2306"></a>
<FONT color="green">2307</FONT>            if (xa &gt; 3294198.0) {<a name="line.2307"></a>
<FONT color="green">2308</FONT>                // PI * (2**20)<a name="line.2308"></a>
<FONT color="green">2309</FONT>                // Argument too big for CodyWaite reduction.  Must use<a name="line.2309"></a>
<FONT color="green">2310</FONT>                // PayneHanek.<a name="line.2310"></a>
<FONT color="green">2311</FONT>                double reduceResults[] = new double[3];<a name="line.2311"></a>
<FONT color="green">2312</FONT>                reducePayneHanek(xa, reduceResults);<a name="line.2312"></a>
<FONT color="green">2313</FONT>                quadrant = ((int) reduceResults[0]) &amp; 3;<a name="line.2313"></a>
<FONT color="green">2314</FONT>                xa = reduceResults[1];<a name="line.2314"></a>
<FONT color="green">2315</FONT>                xb = reduceResults[2];<a name="line.2315"></a>
<FONT color="green">2316</FONT>            } else if (xa &gt; 1.5707963267948966) {<a name="line.2316"></a>
<FONT color="green">2317</FONT>                final CodyWaite cw = new CodyWaite(xa);<a name="line.2317"></a>
<FONT color="green">2318</FONT>                quadrant = cw.getK() &amp; 3;<a name="line.2318"></a>
<FONT color="green">2319</FONT>                xa = cw.getRemA();<a name="line.2319"></a>
<FONT color="green">2320</FONT>                xb = cw.getRemB();<a name="line.2320"></a>
<FONT color="green">2321</FONT>            }<a name="line.2321"></a>
<FONT color="green">2322</FONT>    <a name="line.2322"></a>
<FONT color="green">2323</FONT>            //if (negative)<a name="line.2323"></a>
<FONT color="green">2324</FONT>            //  quadrant = (quadrant + 2) % 4;<a name="line.2324"></a>
<FONT color="green">2325</FONT>    <a name="line.2325"></a>
<FONT color="green">2326</FONT>            switch (quadrant) {<a name="line.2326"></a>
<FONT color="green">2327</FONT>                case 0:<a name="line.2327"></a>
<FONT color="green">2328</FONT>                    return cosQ(xa, xb);<a name="line.2328"></a>
<FONT color="green">2329</FONT>                case 1:<a name="line.2329"></a>
<FONT color="green">2330</FONT>                    return -sinQ(xa, xb);<a name="line.2330"></a>
<FONT color="green">2331</FONT>                case 2:<a name="line.2331"></a>
<FONT color="green">2332</FONT>                    return -cosQ(xa, xb);<a name="line.2332"></a>
<FONT color="green">2333</FONT>                case 3:<a name="line.2333"></a>
<FONT color="green">2334</FONT>                    return sinQ(xa, xb);<a name="line.2334"></a>
<FONT color="green">2335</FONT>                default:<a name="line.2335"></a>
<FONT color="green">2336</FONT>                    return Double.NaN;<a name="line.2336"></a>
<FONT color="green">2337</FONT>            }<a name="line.2337"></a>
<FONT color="green">2338</FONT>        }<a name="line.2338"></a>
<FONT color="green">2339</FONT>    <a name="line.2339"></a>
<FONT color="green">2340</FONT>        /**<a name="line.2340"></a>
<FONT color="green">2341</FONT>         * Tangent function.<a name="line.2341"></a>
<FONT color="green">2342</FONT>         *<a name="line.2342"></a>
<FONT color="green">2343</FONT>         * @param x Argument.<a name="line.2343"></a>
<FONT color="green">2344</FONT>         * @return tan(x)<a name="line.2344"></a>
<FONT color="green">2345</FONT>         */<a name="line.2345"></a>
<FONT color="green">2346</FONT>        public static double tan(double x) {<a name="line.2346"></a>
<FONT color="green">2347</FONT>            boolean negative = false;<a name="line.2347"></a>
<FONT color="green">2348</FONT>            int quadrant = 0;<a name="line.2348"></a>
<FONT color="green">2349</FONT>    <a name="line.2349"></a>
<FONT color="green">2350</FONT>            /* Take absolute value of the input */<a name="line.2350"></a>
<FONT color="green">2351</FONT>            double xa = x;<a name="line.2351"></a>
<FONT color="green">2352</FONT>            if (x &lt; 0) {<a name="line.2352"></a>
<FONT color="green">2353</FONT>                negative = true;<a name="line.2353"></a>
<FONT color="green">2354</FONT>                xa = -xa;<a name="line.2354"></a>
<FONT color="green">2355</FONT>            }<a name="line.2355"></a>
<FONT color="green">2356</FONT>    <a name="line.2356"></a>
<FONT color="green">2357</FONT>            /* Check for zero and negative zero */<a name="line.2357"></a>
<FONT color="green">2358</FONT>            if (xa == 0.0) {<a name="line.2358"></a>
<FONT color="green">2359</FONT>                long bits = Double.doubleToLongBits(x);<a name="line.2359"></a>
<FONT color="green">2360</FONT>                if (bits &lt; 0) {<a name="line.2360"></a>
<FONT color="green">2361</FONT>                    return -0.0;<a name="line.2361"></a>
<FONT color="green">2362</FONT>                }<a name="line.2362"></a>
<FONT color="green">2363</FONT>                return 0.0;<a name="line.2363"></a>
<FONT color="green">2364</FONT>            }<a name="line.2364"></a>
<FONT color="green">2365</FONT>    <a name="line.2365"></a>
<FONT color="green">2366</FONT>            if (xa != xa || xa == Double.POSITIVE_INFINITY) {<a name="line.2366"></a>
<FONT color="green">2367</FONT>                return Double.NaN;<a name="line.2367"></a>
<FONT color="green">2368</FONT>            }<a name="line.2368"></a>
<FONT color="green">2369</FONT>    <a name="line.2369"></a>
<FONT color="green">2370</FONT>            /* Perform any argument reduction */<a name="line.2370"></a>
<FONT color="green">2371</FONT>            double xb = 0;<a name="line.2371"></a>
<FONT color="green">2372</FONT>            if (xa &gt; 3294198.0) {<a name="line.2372"></a>
<FONT color="green">2373</FONT>                // PI * (2**20)<a name="line.2373"></a>
<FONT color="green">2374</FONT>                // Argument too big for CodyWaite reduction.  Must use<a name="line.2374"></a>
<FONT color="green">2375</FONT>                // PayneHanek.<a name="line.2375"></a>
<FONT color="green">2376</FONT>                double reduceResults[] = new double[3];<a name="line.2376"></a>
<FONT color="green">2377</FONT>                reducePayneHanek(xa, reduceResults);<a name="line.2377"></a>
<FONT color="green">2378</FONT>                quadrant = ((int) reduceResults[0]) &amp; 3;<a name="line.2378"></a>
<FONT color="green">2379</FONT>                xa = reduceResults[1];<a name="line.2379"></a>
<FONT color="green">2380</FONT>                xb = reduceResults[2];<a name="line.2380"></a>
<FONT color="green">2381</FONT>            } else if (xa &gt; 1.5707963267948966) {<a name="line.2381"></a>
<FONT color="green">2382</FONT>                final CodyWaite cw = new CodyWaite(xa);<a name="line.2382"></a>
<FONT color="green">2383</FONT>                quadrant = cw.getK() &amp; 3;<a name="line.2383"></a>
<FONT color="green">2384</FONT>                xa = cw.getRemA();<a name="line.2384"></a>
<FONT color="green">2385</FONT>                xb = cw.getRemB();<a name="line.2385"></a>
<FONT color="green">2386</FONT>            }<a name="line.2386"></a>
<FONT color="green">2387</FONT>    <a name="line.2387"></a>
<FONT color="green">2388</FONT>            if (xa &gt; 1.5) {<a name="line.2388"></a>
<FONT color="green">2389</FONT>                // Accuracy suffers between 1.5 and PI/2<a name="line.2389"></a>
<FONT color="green">2390</FONT>                final double pi2a = 1.5707963267948966;<a name="line.2390"></a>
<FONT color="green">2391</FONT>                final double pi2b = 6.123233995736766E-17;<a name="line.2391"></a>
<FONT color="green">2392</FONT>    <a name="line.2392"></a>
<FONT color="green">2393</FONT>                final double a = pi2a - xa;<a name="line.2393"></a>
<FONT color="green">2394</FONT>                double b = -(a - pi2a + xa);<a name="line.2394"></a>
<FONT color="green">2395</FONT>                b += pi2b - xb;<a name="line.2395"></a>
<FONT color="green">2396</FONT>    <a name="line.2396"></a>
<FONT color="green">2397</FONT>                xa = a + b;<a name="line.2397"></a>
<FONT color="green">2398</FONT>                xb = -(xa - a - b);<a name="line.2398"></a>
<FONT color="green">2399</FONT>                quadrant ^= 1;<a name="line.2399"></a>
<FONT color="green">2400</FONT>                negative ^= true;<a name="line.2400"></a>
<FONT color="green">2401</FONT>            }<a name="line.2401"></a>
<FONT color="green">2402</FONT>    <a name="line.2402"></a>
<FONT color="green">2403</FONT>            double result;<a name="line.2403"></a>
<FONT color="green">2404</FONT>            if ((quadrant &amp; 1) == 0) {<a name="line.2404"></a>
<FONT color="green">2405</FONT>                result = tanQ(xa, xb, false);<a name="line.2405"></a>
<FONT color="green">2406</FONT>            } else {<a name="line.2406"></a>
<FONT color="green">2407</FONT>                result = -tanQ(xa, xb, true);<a name="line.2407"></a>
<FONT color="green">2408</FONT>            }<a name="line.2408"></a>
<FONT color="green">2409</FONT>    <a name="line.2409"></a>
<FONT color="green">2410</FONT>            if (negative) {<a name="line.2410"></a>
<FONT color="green">2411</FONT>                result = -result;<a name="line.2411"></a>
<FONT color="green">2412</FONT>            }<a name="line.2412"></a>
<FONT color="green">2413</FONT>    <a name="line.2413"></a>
<FONT color="green">2414</FONT>            return result;<a name="line.2414"></a>
<FONT color="green">2415</FONT>        }<a name="line.2415"></a>
<FONT color="green">2416</FONT>    <a name="line.2416"></a>
<FONT color="green">2417</FONT>        /**<a name="line.2417"></a>
<FONT color="green">2418</FONT>         * Arctangent function<a name="line.2418"></a>
<FONT color="green">2419</FONT>         *  @param x a number<a name="line.2419"></a>
<FONT color="green">2420</FONT>         *  @return atan(x)<a name="line.2420"></a>
<FONT color="green">2421</FONT>         */<a name="line.2421"></a>
<FONT color="green">2422</FONT>        public static double atan(double x) {<a name="line.2422"></a>
<FONT color="green">2423</FONT>            return atan(x, 0.0, false);<a name="line.2423"></a>
<FONT color="green">2424</FONT>        }<a name="line.2424"></a>
<FONT color="green">2425</FONT>    <a name="line.2425"></a>
<FONT color="green">2426</FONT>        /** Internal helper function to compute arctangent.<a name="line.2426"></a>
<FONT color="green">2427</FONT>         * @param xa number from which arctangent is requested<a name="line.2427"></a>
<FONT color="green">2428</FONT>         * @param xb extra bits for x (may be 0.0)<a name="line.2428"></a>
<FONT color="green">2429</FONT>         * @param leftPlane if true, result angle must be put in the left half plane<a name="line.2429"></a>
<FONT color="green">2430</FONT>         * @return atan(xa + xb) (or angle shifted by {@code PI} if leftPlane is true)<a name="line.2430"></a>
<FONT color="green">2431</FONT>         */<a name="line.2431"></a>
<FONT color="green">2432</FONT>        private static double atan(double xa, double xb, boolean leftPlane) {<a name="line.2432"></a>
<FONT color="green">2433</FONT>            boolean negate = false;<a name="line.2433"></a>
<FONT color="green">2434</FONT>            int idx;<a name="line.2434"></a>
<FONT color="green">2435</FONT>    <a name="line.2435"></a>
<FONT color="green">2436</FONT>            if (xa == 0.0) { // Matches +/- 0.0; return correct sign<a name="line.2436"></a>
<FONT color="green">2437</FONT>                return leftPlane ? copySign(Math.PI, xa) : xa;<a name="line.2437"></a>
<FONT color="green">2438</FONT>            }<a name="line.2438"></a>
<FONT color="green">2439</FONT>    <a name="line.2439"></a>
<FONT color="green">2440</FONT>            if (xa &lt; 0) {<a name="line.2440"></a>
<FONT color="green">2441</FONT>                // negative<a name="line.2441"></a>
<FONT color="green">2442</FONT>                xa = -xa;<a name="line.2442"></a>
<FONT color="green">2443</FONT>                xb = -xb;<a name="line.2443"></a>
<FONT color="green">2444</FONT>                negate = true;<a name="line.2444"></a>
<FONT color="green">2445</FONT>            }<a name="line.2445"></a>
<FONT color="green">2446</FONT>    <a name="line.2446"></a>
<FONT color="green">2447</FONT>            if (xa &gt; 1.633123935319537E16) { // Very large input<a name="line.2447"></a>
<FONT color="green">2448</FONT>                return (negate ^ leftPlane) ? (-Math.PI * F_1_2) : (Math.PI * F_1_2);<a name="line.2448"></a>
<FONT color="green">2449</FONT>            }<a name="line.2449"></a>
<FONT color="green">2450</FONT>    <a name="line.2450"></a>
<FONT color="green">2451</FONT>            /* Estimate the closest tabulated arctan value, compute eps = xa-tangentTable */<a name="line.2451"></a>
<FONT color="green">2452</FONT>            if (xa &lt; 1) {<a name="line.2452"></a>
<FONT color="green">2453</FONT>                idx = (int) (((-1.7168146928204136 * xa * xa + 8.0) * xa) + 0.5);<a name="line.2453"></a>
<FONT color="green">2454</FONT>            } else {<a name="line.2454"></a>
<FONT color="green">2455</FONT>                final double oneOverXa = 1 / xa;<a name="line.2455"></a>
<FONT color="green">2456</FONT>                idx = (int) (-((-1.7168146928204136 * oneOverXa * oneOverXa + 8.0) * oneOverXa) + 13.07);<a name="line.2456"></a>
<FONT color="green">2457</FONT>            }<a name="line.2457"></a>
<FONT color="green">2458</FONT>            double epsA = xa - TANGENT_TABLE_A[idx];<a name="line.2458"></a>
<FONT color="green">2459</FONT>            double epsB = -(epsA - xa + TANGENT_TABLE_A[idx]);<a name="line.2459"></a>
<FONT color="green">2460</FONT>            epsB += xb - TANGENT_TABLE_B[idx];<a name="line.2460"></a>
<FONT color="green">2461</FONT>    <a name="line.2461"></a>
<FONT color="green">2462</FONT>            double temp = epsA + epsB;<a name="line.2462"></a>
<FONT color="green">2463</FONT>            epsB = -(temp - epsA - epsB);<a name="line.2463"></a>
<FONT color="green">2464</FONT>            epsA = temp;<a name="line.2464"></a>
<FONT color="green">2465</FONT>    <a name="line.2465"></a>
<FONT color="green">2466</FONT>            /* Compute eps = eps / (1.0 + xa*tangent) */<a name="line.2466"></a>
<FONT color="green">2467</FONT>            temp = xa * HEX_40000000;<a name="line.2467"></a>
<FONT color="green">2468</FONT>            double ya = xa + temp - temp;<a name="line.2468"></a>
<FONT color="green">2469</FONT>            double yb = xb + xa - ya;<a name="line.2469"></a>
<FONT color="green">2470</FONT>            xa = ya;<a name="line.2470"></a>
<FONT color="green">2471</FONT>            xb += yb;<a name="line.2471"></a>
<FONT color="green">2472</FONT>    <a name="line.2472"></a>
<FONT color="green">2473</FONT>            //if (idx &gt; 8 || idx == 0)<a name="line.2473"></a>
<FONT color="green">2474</FONT>            if (idx == 0) {<a name="line.2474"></a>
<FONT color="green">2475</FONT>                /* If the slope of the arctan is gentle enough (&lt; 0.45), this approximation will suffice */<a name="line.2475"></a>
<FONT color="green">2476</FONT>                //double denom = 1.0 / (1.0 + xa*tangentTableA[idx] + xb*tangentTableA[idx] + xa*tangentTableB[idx] + xb*tangentTableB[idx]);<a name="line.2476"></a>
<FONT color="green">2477</FONT>                final double denom = 1d / (1d + (xa + xb) * (TANGENT_TABLE_A[idx] + TANGENT_TABLE_B[idx]));<a name="line.2477"></a>
<FONT color="green">2478</FONT>                //double denom = 1.0 / (1.0 + xa*tangentTableA[idx]);<a name="line.2478"></a>
<FONT color="green">2479</FONT>                ya = epsA * denom;<a name="line.2479"></a>
<FONT color="green">2480</FONT>                yb = epsB * denom;<a name="line.2480"></a>
<FONT color="green">2481</FONT>            } else {<a name="line.2481"></a>
<FONT color="green">2482</FONT>                double temp2 = xa * TANGENT_TABLE_A[idx];<a name="line.2482"></a>
<FONT color="green">2483</FONT>                double za = 1d + temp2;<a name="line.2483"></a>
<FONT color="green">2484</FONT>                double zb = -(za - 1d - temp2);<a name="line.2484"></a>
<FONT color="green">2485</FONT>                temp2 = xb * TANGENT_TABLE_A[idx] + xa * TANGENT_TABLE_B[idx];<a name="line.2485"></a>
<FONT color="green">2486</FONT>                temp = za + temp2;<a name="line.2486"></a>
<FONT color="green">2487</FONT>                zb += -(temp - za - temp2);<a name="line.2487"></a>
<FONT color="green">2488</FONT>                za = temp;<a name="line.2488"></a>
<FONT color="green">2489</FONT>    <a name="line.2489"></a>
<FONT color="green">2490</FONT>                zb += xb * TANGENT_TABLE_B[idx];<a name="line.2490"></a>
<FONT color="green">2491</FONT>                ya = epsA / za;<a name="line.2491"></a>
<FONT color="green">2492</FONT>    <a name="line.2492"></a>
<FONT color="green">2493</FONT>                temp = ya * HEX_40000000;<a name="line.2493"></a>
<FONT color="green">2494</FONT>                final double yaa = (ya + temp) - temp;<a name="line.2494"></a>
<FONT color="green">2495</FONT>                final double yab = ya - yaa;<a name="line.2495"></a>
<FONT color="green">2496</FONT>    <a name="line.2496"></a>
<FONT color="green">2497</FONT>                temp = za * HEX_40000000;<a name="line.2497"></a>
<FONT color="green">2498</FONT>                final double zaa = (za + temp) - temp;<a name="line.2498"></a>
<FONT color="green">2499</FONT>                final double zab = za - zaa;<a name="line.2499"></a>
<FONT color="green">2500</FONT>    <a name="line.2500"></a>
<FONT color="green">2501</FONT>                /* Correct for rounding in division */<a name="line.2501"></a>
<FONT color="green">2502</FONT>                yb = (epsA - yaa * zaa - yaa * zab - yab * zaa - yab * zab) / za;<a name="line.2502"></a>
<FONT color="green">2503</FONT>    <a name="line.2503"></a>
<FONT color="green">2504</FONT>                yb += -epsA * zb / za / za;<a name="line.2504"></a>
<FONT color="green">2505</FONT>                yb += epsB / za;<a name="line.2505"></a>
<FONT color="green">2506</FONT>            }<a name="line.2506"></a>
<FONT color="green">2507</FONT>    <a name="line.2507"></a>
<FONT color="green">2508</FONT>    <a name="line.2508"></a>
<FONT color="green">2509</FONT>            epsA = ya;<a name="line.2509"></a>
<FONT color="green">2510</FONT>            epsB = yb;<a name="line.2510"></a>
<FONT color="green">2511</FONT>    <a name="line.2511"></a>
<FONT color="green">2512</FONT>            /* Evaluate polynomial */<a name="line.2512"></a>
<FONT color="green">2513</FONT>            final double epsA2 = epsA * epsA;<a name="line.2513"></a>
<FONT color="green">2514</FONT>    <a name="line.2514"></a>
<FONT color="green">2515</FONT>            /*<a name="line.2515"></a>
<FONT color="green">2516</FONT>        yb = -0.09001346640161823;<a name="line.2516"></a>
<FONT color="green">2517</FONT>        yb = yb * epsA2 + 0.11110718400605211;<a name="line.2517"></a>
<FONT color="green">2518</FONT>        yb = yb * epsA2 + -0.1428571349122913;<a name="line.2518"></a>
<FONT color="green">2519</FONT>        yb = yb * epsA2 + 0.19999999999273194;<a name="line.2519"></a>
<FONT color="green">2520</FONT>        yb = yb * epsA2 + -0.33333333333333093;<a name="line.2520"></a>
<FONT color="green">2521</FONT>        yb = yb * epsA2 * epsA;<a name="line.2521"></a>
<FONT color="green">2522</FONT>             */<a name="line.2522"></a>
<FONT color="green">2523</FONT>    <a name="line.2523"></a>
<FONT color="green">2524</FONT>            yb = 0.07490822288864472;<a name="line.2524"></a>
<FONT color="green">2525</FONT>            yb = yb * epsA2 + -0.09088450866185192;<a name="line.2525"></a>
<FONT color="green">2526</FONT>            yb = yb * epsA2 + 0.11111095942313305;<a name="line.2526"></a>
<FONT color="green">2527</FONT>            yb = yb * epsA2 + -0.1428571423679182;<a name="line.2527"></a>
<FONT color="green">2528</FONT>            yb = yb * epsA2 + 0.19999999999923582;<a name="line.2528"></a>
<FONT color="green">2529</FONT>            yb = yb * epsA2 + -0.33333333333333287;<a name="line.2529"></a>
<FONT color="green">2530</FONT>            yb = yb * epsA2 * epsA;<a name="line.2530"></a>
<FONT color="green">2531</FONT>    <a name="line.2531"></a>
<FONT color="green">2532</FONT>    <a name="line.2532"></a>
<FONT color="green">2533</FONT>            ya = epsA;<a name="line.2533"></a>
<FONT color="green">2534</FONT>    <a name="line.2534"></a>
<FONT color="green">2535</FONT>            temp = ya + yb;<a name="line.2535"></a>
<FONT color="green">2536</FONT>            yb = -(temp - ya - yb);<a name="line.2536"></a>
<FONT color="green">2537</FONT>            ya = temp;<a name="line.2537"></a>
<FONT color="green">2538</FONT>    <a name="line.2538"></a>
<FONT color="green">2539</FONT>            /* Add in effect of epsB.   atan'(x) = 1/(1+x^2) */<a name="line.2539"></a>
<FONT color="green">2540</FONT>            yb += epsB / (1d + epsA * epsA);<a name="line.2540"></a>
<FONT color="green">2541</FONT>    <a name="line.2541"></a>
<FONT color="green">2542</FONT>            //result = yb + eighths[idx] + ya;<a name="line.2542"></a>
<FONT color="green">2543</FONT>            double za = EIGHTHS[idx] + ya;<a name="line.2543"></a>
<FONT color="green">2544</FONT>            double zb = -(za - EIGHTHS[idx] - ya);<a name="line.2544"></a>
<FONT color="green">2545</FONT>            temp = za + yb;<a name="line.2545"></a>
<FONT color="green">2546</FONT>            zb += -(temp - za - yb);<a name="line.2546"></a>
<FONT color="green">2547</FONT>            za = temp;<a name="line.2547"></a>
<FONT color="green">2548</FONT>    <a name="line.2548"></a>
<FONT color="green">2549</FONT>            double result = za + zb;<a name="line.2549"></a>
<FONT color="green">2550</FONT>            double resultb = -(result - za - zb);<a name="line.2550"></a>
<FONT color="green">2551</FONT>    <a name="line.2551"></a>
<FONT color="green">2552</FONT>            if (leftPlane) {<a name="line.2552"></a>
<FONT color="green">2553</FONT>                // Result is in the left plane<a name="line.2553"></a>
<FONT color="green">2554</FONT>                final double pia = 1.5707963267948966 * 2;<a name="line.2554"></a>
<FONT color="green">2555</FONT>                final double pib = 6.123233995736766E-17 * 2;<a name="line.2555"></a>
<FONT color="green">2556</FONT>    <a name="line.2556"></a>
<FONT color="green">2557</FONT>                za = pia - result;<a name="line.2557"></a>
<FONT color="green">2558</FONT>                zb = -(za - pia + result);<a name="line.2558"></a>
<FONT color="green">2559</FONT>                zb += pib - resultb;<a name="line.2559"></a>
<FONT color="green">2560</FONT>    <a name="line.2560"></a>
<FONT color="green">2561</FONT>                result = za + zb;<a name="line.2561"></a>
<FONT color="green">2562</FONT>                resultb = -(result - za - zb);<a name="line.2562"></a>
<FONT color="green">2563</FONT>            }<a name="line.2563"></a>
<FONT color="green">2564</FONT>    <a name="line.2564"></a>
<FONT color="green">2565</FONT>    <a name="line.2565"></a>
<FONT color="green">2566</FONT>            if (negate ^ leftPlane) {<a name="line.2566"></a>
<FONT color="green">2567</FONT>                result = -result;<a name="line.2567"></a>
<FONT color="green">2568</FONT>            }<a name="line.2568"></a>
<FONT color="green">2569</FONT>    <a name="line.2569"></a>
<FONT color="green">2570</FONT>            return result;<a name="line.2570"></a>
<FONT color="green">2571</FONT>        }<a name="line.2571"></a>
<FONT color="green">2572</FONT>    <a name="line.2572"></a>
<FONT color="green">2573</FONT>        /**<a name="line.2573"></a>
<FONT color="green">2574</FONT>         * Two arguments arctangent function<a name="line.2574"></a>
<FONT color="green">2575</FONT>         * @param y ordinate<a name="line.2575"></a>
<FONT color="green">2576</FONT>         * @param x abscissa<a name="line.2576"></a>
<FONT color="green">2577</FONT>         * @return phase angle of point (x,y) between {@code -PI} and {@code PI}<a name="line.2577"></a>
<FONT color="green">2578</FONT>         */<a name="line.2578"></a>
<FONT color="green">2579</FONT>        public static double atan2(double y, double x) {<a name="line.2579"></a>
<FONT color="green">2580</FONT>            if (x != x || y != y) {<a name="line.2580"></a>
<FONT color="green">2581</FONT>                return Double.NaN;<a name="line.2581"></a>
<FONT color="green">2582</FONT>            }<a name="line.2582"></a>
<FONT color="green">2583</FONT>    <a name="line.2583"></a>
<FONT color="green">2584</FONT>            if (y == 0) {<a name="line.2584"></a>
<FONT color="green">2585</FONT>                final double result = x * y;<a name="line.2585"></a>
<FONT color="green">2586</FONT>                final double invx = 1d / x;<a name="line.2586"></a>
<FONT color="green">2587</FONT>                final double invy = 1d / y;<a name="line.2587"></a>
<FONT color="green">2588</FONT>    <a name="line.2588"></a>
<FONT color="green">2589</FONT>                if (invx == 0) { // X is infinite<a name="line.2589"></a>
<FONT color="green">2590</FONT>                    if (x &gt; 0) {<a name="line.2590"></a>
<FONT color="green">2591</FONT>                        return y; // return +/- 0.0<a name="line.2591"></a>
<FONT color="green">2592</FONT>                    } else {<a name="line.2592"></a>
<FONT color="green">2593</FONT>                        return copySign(Math.PI, y);<a name="line.2593"></a>
<FONT color="green">2594</FONT>                    }<a name="line.2594"></a>
<FONT color="green">2595</FONT>                }<a name="line.2595"></a>
<FONT color="green">2596</FONT>    <a name="line.2596"></a>
<FONT color="green">2597</FONT>                if (x &lt; 0 || invx &lt; 0) {<a name="line.2597"></a>
<FONT color="green">2598</FONT>                    if (y &lt; 0 || invy &lt; 0) {<a name="line.2598"></a>
<FONT color="green">2599</FONT>                        return -Math.PI;<a name="line.2599"></a>
<FONT color="green">2600</FONT>                    } else {<a name="line.2600"></a>
<FONT color="green">2601</FONT>                        return Math.PI;<a name="line.2601"></a>
<FONT color="green">2602</FONT>                    }<a name="line.2602"></a>
<FONT color="green">2603</FONT>                } else {<a name="line.2603"></a>
<FONT color="green">2604</FONT>                    return result;<a name="line.2604"></a>
<FONT color="green">2605</FONT>                }<a name="line.2605"></a>
<FONT color="green">2606</FONT>            }<a name="line.2606"></a>
<FONT color="green">2607</FONT>    <a name="line.2607"></a>
<FONT color="green">2608</FONT>            // y cannot now be zero<a name="line.2608"></a>
<FONT color="green">2609</FONT>    <a name="line.2609"></a>
<FONT color="green">2610</FONT>            if (y == Double.POSITIVE_INFINITY) {<a name="line.2610"></a>
<FONT color="green">2611</FONT>                if (x == Double.POSITIVE_INFINITY) {<a name="line.2611"></a>
<FONT color="green">2612</FONT>                    return Math.PI * F_1_4;<a name="line.2612"></a>
<FONT color="green">2613</FONT>                }<a name="line.2613"></a>
<FONT color="green">2614</FONT>    <a name="line.2614"></a>
<FONT color="green">2615</FONT>                if (x == Double.NEGATIVE_INFINITY) {<a name="line.2615"></a>
<FONT color="green">2616</FONT>                    return Math.PI * F_3_4;<a name="line.2616"></a>
<FONT color="green">2617</FONT>                }<a name="line.2617"></a>
<FONT color="green">2618</FONT>    <a name="line.2618"></a>
<FONT color="green">2619</FONT>                return Math.PI * F_1_2;<a name="line.2619"></a>
<FONT color="green">2620</FONT>            }<a name="line.2620"></a>
<FONT color="green">2621</FONT>    <a name="line.2621"></a>
<FONT color="green">2622</FONT>            if (y == Double.NEGATIVE_INFINITY) {<a name="line.2622"></a>
<FONT color="green">2623</FONT>                if (x == Double.POSITIVE_INFINITY) {<a name="line.2623"></a>
<FONT color="green">2624</FONT>                    return -Math.PI * F_1_4;<a name="line.2624"></a>
<FONT color="green">2625</FONT>                }<a name="line.2625"></a>
<FONT color="green">2626</FONT>    <a name="line.2626"></a>
<FONT color="green">2627</FONT>                if (x == Double.NEGATIVE_INFINITY) {<a name="line.2627"></a>
<FONT color="green">2628</FONT>                    return -Math.PI * F_3_4;<a name="line.2628"></a>
<FONT color="green">2629</FONT>                }<a name="line.2629"></a>
<FONT color="green">2630</FONT>    <a name="line.2630"></a>
<FONT color="green">2631</FONT>                return -Math.PI * F_1_2;<a name="line.2631"></a>
<FONT color="green">2632</FONT>            }<a name="line.2632"></a>
<FONT color="green">2633</FONT>    <a name="line.2633"></a>
<FONT color="green">2634</FONT>            if (x == Double.POSITIVE_INFINITY) {<a name="line.2634"></a>
<FONT color="green">2635</FONT>                if (y &gt; 0 || 1 / y &gt; 0) {<a name="line.2635"></a>
<FONT color="green">2636</FONT>                    return 0d;<a name="line.2636"></a>
<FONT color="green">2637</FONT>                }<a name="line.2637"></a>
<FONT color="green">2638</FONT>    <a name="line.2638"></a>
<FONT color="green">2639</FONT>                if (y &lt; 0 || 1 / y &lt; 0) {<a name="line.2639"></a>
<FONT color="green">2640</FONT>                    return -0d;<a name="line.2640"></a>
<FONT color="green">2641</FONT>                }<a name="line.2641"></a>
<FONT color="green">2642</FONT>            }<a name="line.2642"></a>
<FONT color="green">2643</FONT>    <a name="line.2643"></a>
<FONT color="green">2644</FONT>            if (x == Double.NEGATIVE_INFINITY)<a name="line.2644"></a>
<FONT color="green">2645</FONT>            {<a name="line.2645"></a>
<FONT color="green">2646</FONT>                if (y &gt; 0.0 || 1 / y &gt; 0.0) {<a name="line.2646"></a>
<FONT color="green">2647</FONT>                    return Math.PI;<a name="line.2647"></a>
<FONT color="green">2648</FONT>                }<a name="line.2648"></a>
<FONT color="green">2649</FONT>    <a name="line.2649"></a>
<FONT color="green">2650</FONT>                if (y &lt; 0 || 1 / y &lt; 0) {<a name="line.2650"></a>
<FONT color="green">2651</FONT>                    return -Math.PI;<a name="line.2651"></a>
<FONT color="green">2652</FONT>                }<a name="line.2652"></a>
<FONT color="green">2653</FONT>            }<a name="line.2653"></a>
<FONT color="green">2654</FONT>    <a name="line.2654"></a>
<FONT color="green">2655</FONT>            // Neither y nor x can be infinite or NAN here<a name="line.2655"></a>
<FONT color="green">2656</FONT>    <a name="line.2656"></a>
<FONT color="green">2657</FONT>            if (x == 0) {<a name="line.2657"></a>
<FONT color="green">2658</FONT>                if (y &gt; 0 || 1 / y &gt; 0) {<a name="line.2658"></a>
<FONT color="green">2659</FONT>                    return Math.PI * F_1_2;<a name="line.2659"></a>
<FONT color="green">2660</FONT>                }<a name="line.2660"></a>
<FONT color="green">2661</FONT>    <a name="line.2661"></a>
<FONT color="green">2662</FONT>                if (y &lt; 0 || 1 / y &lt; 0) {<a name="line.2662"></a>
<FONT color="green">2663</FONT>                    return -Math.PI * F_1_2;<a name="line.2663"></a>
<FONT color="green">2664</FONT>                }<a name="line.2664"></a>
<FONT color="green">2665</FONT>            }<a name="line.2665"></a>
<FONT color="green">2666</FONT>    <a name="line.2666"></a>
<FONT color="green">2667</FONT>            // Compute ratio r = y/x<a name="line.2667"></a>
<FONT color="green">2668</FONT>            final double r = y / x;<a name="line.2668"></a>
<FONT color="green">2669</FONT>            if (Double.isInfinite(r)) { // bypass calculations that can create NaN<a name="line.2669"></a>
<FONT color="green">2670</FONT>                return atan(r, 0, x &lt; 0);<a name="line.2670"></a>
<FONT color="green">2671</FONT>            }<a name="line.2671"></a>
<FONT color="green">2672</FONT>    <a name="line.2672"></a>
<FONT color="green">2673</FONT>            double ra = doubleHighPart(r);<a name="line.2673"></a>
<FONT color="green">2674</FONT>            double rb = r - ra;<a name="line.2674"></a>
<FONT color="green">2675</FONT>    <a name="line.2675"></a>
<FONT color="green">2676</FONT>            // Split x<a name="line.2676"></a>
<FONT color="green">2677</FONT>            final double xa = doubleHighPart(x);<a name="line.2677"></a>
<FONT color="green">2678</FONT>            final double xb = x - xa;<a name="line.2678"></a>
<FONT color="green">2679</FONT>    <a name="line.2679"></a>
<FONT color="green">2680</FONT>            rb += (y - ra * xa - ra * xb - rb * xa - rb * xb) / x;<a name="line.2680"></a>
<FONT color="green">2681</FONT>    <a name="line.2681"></a>
<FONT color="green">2682</FONT>            final double temp = ra + rb;<a name="line.2682"></a>
<FONT color="green">2683</FONT>            rb = -(temp - ra - rb);<a name="line.2683"></a>
<FONT color="green">2684</FONT>            ra = temp;<a name="line.2684"></a>
<FONT color="green">2685</FONT>    <a name="line.2685"></a>
<FONT color="green">2686</FONT>            if (ra == 0) { // Fix up the sign so atan works correctly<a name="line.2686"></a>
<FONT color="green">2687</FONT>                ra = copySign(0d, y);<a name="line.2687"></a>
<FONT color="green">2688</FONT>            }<a name="line.2688"></a>
<FONT color="green">2689</FONT>    <a name="line.2689"></a>
<FONT color="green">2690</FONT>            // Call atan<a name="line.2690"></a>
<FONT color="green">2691</FONT>            final double result = atan(ra, rb, x &lt; 0);<a name="line.2691"></a>
<FONT color="green">2692</FONT>    <a name="line.2692"></a>
<FONT color="green">2693</FONT>            return result;<a name="line.2693"></a>
<FONT color="green">2694</FONT>        }<a name="line.2694"></a>
<FONT color="green">2695</FONT>    <a name="line.2695"></a>
<FONT color="green">2696</FONT>        /** Compute the arc sine of a number.<a name="line.2696"></a>
<FONT color="green">2697</FONT>         * @param x number on which evaluation is done<a name="line.2697"></a>
<FONT color="green">2698</FONT>         * @return arc sine of x<a name="line.2698"></a>
<FONT color="green">2699</FONT>         */<a name="line.2699"></a>
<FONT color="green">2700</FONT>        public static double asin(double x) {<a name="line.2700"></a>
<FONT color="green">2701</FONT>          if (x != x) {<a name="line.2701"></a>
<FONT color="green">2702</FONT>              return Double.NaN;<a name="line.2702"></a>
<FONT color="green">2703</FONT>          }<a name="line.2703"></a>
<FONT color="green">2704</FONT>    <a name="line.2704"></a>
<FONT color="green">2705</FONT>          if (x &gt; 1.0 || x &lt; -1.0) {<a name="line.2705"></a>
<FONT color="green">2706</FONT>              return Double.NaN;<a name="line.2706"></a>
<FONT color="green">2707</FONT>          }<a name="line.2707"></a>
<FONT color="green">2708</FONT>    <a name="line.2708"></a>
<FONT color="green">2709</FONT>          if (x == 1.0) {<a name="line.2709"></a>
<FONT color="green">2710</FONT>              return Math.PI/2.0;<a name="line.2710"></a>
<FONT color="green">2711</FONT>          }<a name="line.2711"></a>
<FONT color="green">2712</FONT>    <a name="line.2712"></a>
<FONT color="green">2713</FONT>          if (x == -1.0) {<a name="line.2713"></a>
<FONT color="green">2714</FONT>              return -Math.PI/2.0;<a name="line.2714"></a>
<FONT color="green">2715</FONT>          }<a name="line.2715"></a>
<FONT color="green">2716</FONT>    <a name="line.2716"></a>
<FONT color="green">2717</FONT>          if (x == 0.0) { // Matches +/- 0.0; return correct sign<a name="line.2717"></a>
<FONT color="green">2718</FONT>              return x;<a name="line.2718"></a>
<FONT color="green">2719</FONT>          }<a name="line.2719"></a>
<FONT color="green">2720</FONT>    <a name="line.2720"></a>
<FONT color="green">2721</FONT>          /* Compute asin(x) = atan(x/sqrt(1-x*x)) */<a name="line.2721"></a>
<FONT color="green">2722</FONT>    <a name="line.2722"></a>
<FONT color="green">2723</FONT>          /* Split x */<a name="line.2723"></a>
<FONT color="green">2724</FONT>          double temp = x * HEX_40000000;<a name="line.2724"></a>
<FONT color="green">2725</FONT>          final double xa = x + temp - temp;<a name="line.2725"></a>
<FONT color="green">2726</FONT>          final double xb = x - xa;<a name="line.2726"></a>
<FONT color="green">2727</FONT>    <a name="line.2727"></a>
<FONT color="green">2728</FONT>          /* Square it */<a name="line.2728"></a>
<FONT color="green">2729</FONT>          double ya = xa*xa;<a name="line.2729"></a>
<FONT color="green">2730</FONT>          double yb = xa*xb*2.0 + xb*xb;<a name="line.2730"></a>
<FONT color="green">2731</FONT>    <a name="line.2731"></a>
<FONT color="green">2732</FONT>          /* Subtract from 1 */<a name="line.2732"></a>
<FONT color="green">2733</FONT>          ya = -ya;<a name="line.2733"></a>
<FONT color="green">2734</FONT>          yb = -yb;<a name="line.2734"></a>
<FONT color="green">2735</FONT>    <a name="line.2735"></a>
<FONT color="green">2736</FONT>          double za = 1.0 + ya;<a name="line.2736"></a>
<FONT color="green">2737</FONT>          double zb = -(za - 1.0 - ya);<a name="line.2737"></a>
<FONT color="green">2738</FONT>    <a name="line.2738"></a>
<FONT color="green">2739</FONT>          temp = za + yb;<a name="line.2739"></a>
<FONT color="green">2740</FONT>          zb += -(temp - za - yb);<a name="line.2740"></a>
<FONT color="green">2741</FONT>          za = temp;<a name="line.2741"></a>
<FONT color="green">2742</FONT>    <a name="line.2742"></a>
<FONT color="green">2743</FONT>          /* Square root */<a name="line.2743"></a>
<FONT color="green">2744</FONT>          double y;<a name="line.2744"></a>
<FONT color="green">2745</FONT>          y = sqrt(za);<a name="line.2745"></a>
<FONT color="green">2746</FONT>          temp = y * HEX_40000000;<a name="line.2746"></a>
<FONT color="green">2747</FONT>          ya = y + temp - temp;<a name="line.2747"></a>
<FONT color="green">2748</FONT>          yb = y - ya;<a name="line.2748"></a>
<FONT color="green">2749</FONT>    <a name="line.2749"></a>
<FONT color="green">2750</FONT>          /* Extend precision of sqrt */<a name="line.2750"></a>
<FONT color="green">2751</FONT>          yb += (za - ya*ya - 2*ya*yb - yb*yb) / (2.0*y);<a name="line.2751"></a>
<FONT color="green">2752</FONT>    <a name="line.2752"></a>
<FONT color="green">2753</FONT>          /* Contribution of zb to sqrt */<a name="line.2753"></a>
<FONT color="green">2754</FONT>          double dx = zb / (2.0*y);<a name="line.2754"></a>
<FONT color="green">2755</FONT>    <a name="line.2755"></a>
<FONT color="green">2756</FONT>          // Compute ratio r = x/y<a name="line.2756"></a>
<FONT color="green">2757</FONT>          double r = x/y;<a name="line.2757"></a>
<FONT color="green">2758</FONT>          temp = r * HEX_40000000;<a name="line.2758"></a>
<FONT color="green">2759</FONT>          double ra = r + temp - temp;<a name="line.2759"></a>
<FONT color="green">2760</FONT>          double rb = r - ra;<a name="line.2760"></a>
<FONT color="green">2761</FONT>    <a name="line.2761"></a>
<FONT color="green">2762</FONT>          rb += (x - ra*ya - ra*yb - rb*ya - rb*yb) / y;  // Correct for rounding in division<a name="line.2762"></a>
<FONT color="green">2763</FONT>          rb += -x * dx / y / y;  // Add in effect additional bits of sqrt.<a name="line.2763"></a>
<FONT color="green">2764</FONT>    <a name="line.2764"></a>
<FONT color="green">2765</FONT>          temp = ra + rb;<a name="line.2765"></a>
<FONT color="green">2766</FONT>          rb = -(temp - ra - rb);<a name="line.2766"></a>
<FONT color="green">2767</FONT>          ra = temp;<a name="line.2767"></a>
<FONT color="green">2768</FONT>    <a name="line.2768"></a>
<FONT color="green">2769</FONT>          return atan(ra, rb, false);<a name="line.2769"></a>
<FONT color="green">2770</FONT>        }<a name="line.2770"></a>
<FONT color="green">2771</FONT>    <a name="line.2771"></a>
<FONT color="green">2772</FONT>        /** Compute the arc cosine of a number.<a name="line.2772"></a>
<FONT color="green">2773</FONT>         * @param x number on which evaluation is done<a name="line.2773"></a>
<FONT color="green">2774</FONT>         * @return arc cosine of x<a name="line.2774"></a>
<FONT color="green">2775</FONT>         */<a name="line.2775"></a>
<FONT color="green">2776</FONT>        public static double acos(double x) {<a name="line.2776"></a>
<FONT color="green">2777</FONT>          if (x != x) {<a name="line.2777"></a>
<FONT color="green">2778</FONT>              return Double.NaN;<a name="line.2778"></a>
<FONT color="green">2779</FONT>          }<a name="line.2779"></a>
<FONT color="green">2780</FONT>    <a name="line.2780"></a>
<FONT color="green">2781</FONT>          if (x &gt; 1.0 || x &lt; -1.0) {<a name="line.2781"></a>
<FONT color="green">2782</FONT>              return Double.NaN;<a name="line.2782"></a>
<FONT color="green">2783</FONT>          }<a name="line.2783"></a>
<FONT color="green">2784</FONT>    <a name="line.2784"></a>
<FONT color="green">2785</FONT>          if (x == -1.0) {<a name="line.2785"></a>
<FONT color="green">2786</FONT>              return Math.PI;<a name="line.2786"></a>
<FONT color="green">2787</FONT>          }<a name="line.2787"></a>
<FONT color="green">2788</FONT>    <a name="line.2788"></a>
<FONT color="green">2789</FONT>          if (x == 1.0) {<a name="line.2789"></a>
<FONT color="green">2790</FONT>              return 0.0;<a name="line.2790"></a>
<FONT color="green">2791</FONT>          }<a name="line.2791"></a>
<FONT color="green">2792</FONT>    <a name="line.2792"></a>
<FONT color="green">2793</FONT>          if (x == 0) {<a name="line.2793"></a>
<FONT color="green">2794</FONT>              return Math.PI/2.0;<a name="line.2794"></a>
<FONT color="green">2795</FONT>          }<a name="line.2795"></a>
<FONT color="green">2796</FONT>    <a name="line.2796"></a>
<FONT color="green">2797</FONT>          /* Compute acos(x) = atan(sqrt(1-x*x)/x) */<a name="line.2797"></a>
<FONT color="green">2798</FONT>    <a name="line.2798"></a>
<FONT color="green">2799</FONT>          /* Split x */<a name="line.2799"></a>
<FONT color="green">2800</FONT>          double temp = x * HEX_40000000;<a name="line.2800"></a>
<FONT color="green">2801</FONT>          final double xa = x + temp - temp;<a name="line.2801"></a>
<FONT color="green">2802</FONT>          final double xb = x - xa;<a name="line.2802"></a>
<FONT color="green">2803</FONT>    <a name="line.2803"></a>
<FONT color="green">2804</FONT>          /* Square it */<a name="line.2804"></a>
<FONT color="green">2805</FONT>          double ya = xa*xa;<a name="line.2805"></a>
<FONT color="green">2806</FONT>          double yb = xa*xb*2.0 + xb*xb;<a name="line.2806"></a>
<FONT color="green">2807</FONT>    <a name="line.2807"></a>
<FONT color="green">2808</FONT>          /* Subtract from 1 */<a name="line.2808"></a>
<FONT color="green">2809</FONT>          ya = -ya;<a name="line.2809"></a>
<FONT color="green">2810</FONT>          yb = -yb;<a name="line.2810"></a>
<FONT color="green">2811</FONT>    <a name="line.2811"></a>
<FONT color="green">2812</FONT>          double za = 1.0 + ya;<a name="line.2812"></a>
<FONT color="green">2813</FONT>          double zb = -(za - 1.0 - ya);<a name="line.2813"></a>
<FONT color="green">2814</FONT>    <a name="line.2814"></a>
<FONT color="green">2815</FONT>          temp = za + yb;<a name="line.2815"></a>
<FONT color="green">2816</FONT>          zb += -(temp - za - yb);<a name="line.2816"></a>
<FONT color="green">2817</FONT>          za = temp;<a name="line.2817"></a>
<FONT color="green">2818</FONT>    <a name="line.2818"></a>
<FONT color="green">2819</FONT>          /* Square root */<a name="line.2819"></a>
<FONT color="green">2820</FONT>          double y = sqrt(za);<a name="line.2820"></a>
<FONT color="green">2821</FONT>          temp = y * HEX_40000000;<a name="line.2821"></a>
<FONT color="green">2822</FONT>          ya = y + temp - temp;<a name="line.2822"></a>
<FONT color="green">2823</FONT>          yb = y - ya;<a name="line.2823"></a>
<FONT color="green">2824</FONT>    <a name="line.2824"></a>
<FONT color="green">2825</FONT>          /* Extend precision of sqrt */<a name="line.2825"></a>
<FONT color="green">2826</FONT>          yb += (za - ya*ya - 2*ya*yb - yb*yb) / (2.0*y);<a name="line.2826"></a>
<FONT color="green">2827</FONT>    <a name="line.2827"></a>
<FONT color="green">2828</FONT>          /* Contribution of zb to sqrt */<a name="line.2828"></a>
<FONT color="green">2829</FONT>          yb += zb / (2.0*y);<a name="line.2829"></a>
<FONT color="green">2830</FONT>          y = ya+yb;<a name="line.2830"></a>
<FONT color="green">2831</FONT>          yb = -(y - ya - yb);<a name="line.2831"></a>
<FONT color="green">2832</FONT>    <a name="line.2832"></a>
<FONT color="green">2833</FONT>          // Compute ratio r = y/x<a name="line.2833"></a>
<FONT color="green">2834</FONT>          double r = y/x;<a name="line.2834"></a>
<FONT color="green">2835</FONT>    <a name="line.2835"></a>
<FONT color="green">2836</FONT>          // Did r overflow?<a name="line.2836"></a>
<FONT color="green">2837</FONT>          if (Double.isInfinite(r)) { // x is effectively zero<a name="line.2837"></a>
<FONT color="green">2838</FONT>              return Math.PI/2; // so return the appropriate value<a name="line.2838"></a>
<FONT color="green">2839</FONT>          }<a name="line.2839"></a>
<FONT color="green">2840</FONT>    <a name="line.2840"></a>
<FONT color="green">2841</FONT>          double ra = doubleHighPart(r);<a name="line.2841"></a>
<FONT color="green">2842</FONT>          double rb = r - ra;<a name="line.2842"></a>
<FONT color="green">2843</FONT>    <a name="line.2843"></a>
<FONT color="green">2844</FONT>          rb += (y - ra*xa - ra*xb - rb*xa - rb*xb) / x;  // Correct for rounding in division<a name="line.2844"></a>
<FONT color="green">2845</FONT>          rb += yb / x;  // Add in effect additional bits of sqrt.<a name="line.2845"></a>
<FONT color="green">2846</FONT>    <a name="line.2846"></a>
<FONT color="green">2847</FONT>          temp = ra + rb;<a name="line.2847"></a>
<FONT color="green">2848</FONT>          rb = -(temp - ra - rb);<a name="line.2848"></a>
<FONT color="green">2849</FONT>          ra = temp;<a name="line.2849"></a>
<FONT color="green">2850</FONT>    <a name="line.2850"></a>
<FONT color="green">2851</FONT>          return atan(ra, rb, x&lt;0);<a name="line.2851"></a>
<FONT color="green">2852</FONT>        }<a name="line.2852"></a>
<FONT color="green">2853</FONT>    <a name="line.2853"></a>
<FONT color="green">2854</FONT>        /** Compute the cubic root of a number.<a name="line.2854"></a>
<FONT color="green">2855</FONT>         * @param x number on which evaluation is done<a name="line.2855"></a>
<FONT color="green">2856</FONT>         * @return cubic root of x<a name="line.2856"></a>
<FONT color="green">2857</FONT>         */<a name="line.2857"></a>
<FONT color="green">2858</FONT>        public static double cbrt(double x) {<a name="line.2858"></a>
<FONT color="green">2859</FONT>          /* Convert input double to bits */<a name="line.2859"></a>
<FONT color="green">2860</FONT>          long inbits = Double.doubleToLongBits(x);<a name="line.2860"></a>
<FONT color="green">2861</FONT>          int exponent = (int) ((inbits &gt;&gt; 52) &amp; 0x7ff) - 1023;<a name="line.2861"></a>
<FONT color="green">2862</FONT>          boolean subnormal = false;<a name="line.2862"></a>
<FONT color="green">2863</FONT>    <a name="line.2863"></a>
<FONT color="green">2864</FONT>          if (exponent == -1023) {<a name="line.2864"></a>
<FONT color="green">2865</FONT>              if (x == 0) {<a name="line.2865"></a>
<FONT color="green">2866</FONT>                  return x;<a name="line.2866"></a>
<FONT color="green">2867</FONT>              }<a name="line.2867"></a>
<FONT color="green">2868</FONT>    <a name="line.2868"></a>
<FONT color="green">2869</FONT>              /* Subnormal, so normalize */<a name="line.2869"></a>
<FONT color="green">2870</FONT>              subnormal = true;<a name="line.2870"></a>
<FONT color="green">2871</FONT>              x *= 1.8014398509481984E16;  // 2^54<a name="line.2871"></a>
<FONT color="green">2872</FONT>              inbits = Double.doubleToLongBits(x);<a name="line.2872"></a>
<FONT color="green">2873</FONT>              exponent = (int) ((inbits &gt;&gt; 52) &amp; 0x7ff) - 1023;<a name="line.2873"></a>
<FONT color="green">2874</FONT>          }<a name="line.2874"></a>
<FONT color="green">2875</FONT>    <a name="line.2875"></a>
<FONT color="green">2876</FONT>          if (exponent == 1024) {<a name="line.2876"></a>
<FONT color="green">2877</FONT>              // Nan or infinity.  Don't care which.<a name="line.2877"></a>
<FONT color="green">2878</FONT>              return x;<a name="line.2878"></a>
<FONT color="green">2879</FONT>          }<a name="line.2879"></a>
<FONT color="green">2880</FONT>    <a name="line.2880"></a>
<FONT color="green">2881</FONT>          /* Divide the exponent by 3 */<a name="line.2881"></a>
<FONT color="green">2882</FONT>          int exp3 = exponent / 3;<a name="line.2882"></a>
<FONT color="green">2883</FONT>    <a name="line.2883"></a>
<FONT color="green">2884</FONT>          /* p2 will be the nearest power of 2 to x with its exponent divided by 3 */<a name="line.2884"></a>
<FONT color="green">2885</FONT>          double p2 = Double.longBitsToDouble((inbits &amp; 0x8000000000000000L) |<a name="line.2885"></a>
<FONT color="green">2886</FONT>                                              (long)(((exp3 + 1023) &amp; 0x7ff)) &lt;&lt; 52);<a name="line.2886"></a>
<FONT color="green">2887</FONT>    <a name="line.2887"></a>
<FONT color="green">2888</FONT>          /* This will be a number between 1 and 2 */<a name="line.2888"></a>
<FONT color="green">2889</FONT>          final double mant = Double.longBitsToDouble((inbits &amp; 0x000fffffffffffffL) | 0x3ff0000000000000L);<a name="line.2889"></a>
<FONT color="green">2890</FONT>    <a name="line.2890"></a>
<FONT color="green">2891</FONT>          /* Estimate the cube root of mant by polynomial */<a name="line.2891"></a>
<FONT color="green">2892</FONT>          double est = -0.010714690733195933;<a name="line.2892"></a>
<FONT color="green">2893</FONT>          est = est * mant + 0.0875862700108075;<a name="line.2893"></a>
<FONT color="green">2894</FONT>          est = est * mant + -0.3058015757857271;<a name="line.2894"></a>
<FONT color="green">2895</FONT>          est = est * mant + 0.7249995199969751;<a name="line.2895"></a>
<FONT color="green">2896</FONT>          est = est * mant + 0.5039018405998233;<a name="line.2896"></a>
<FONT color="green">2897</FONT>    <a name="line.2897"></a>
<FONT color="green">2898</FONT>          est *= CBRTTWO[exponent % 3 + 2];<a name="line.2898"></a>
<FONT color="green">2899</FONT>    <a name="line.2899"></a>
<FONT color="green">2900</FONT>          // est should now be good to about 15 bits of precision.   Do 2 rounds of<a name="line.2900"></a>
<FONT color="green">2901</FONT>          // Newton's method to get closer,  this should get us full double precision<a name="line.2901"></a>
<FONT color="green">2902</FONT>          // Scale down x for the purpose of doing newtons method.  This avoids over/under flows.<a name="line.2902"></a>
<FONT color="green">2903</FONT>          final double xs = x / (p2*p2*p2);<a name="line.2903"></a>
<FONT color="green">2904</FONT>          est += (xs - est*est*est) / (3*est*est);<a name="line.2904"></a>
<FONT color="green">2905</FONT>          est += (xs - est*est*est) / (3*est*est);<a name="line.2905"></a>
<FONT color="green">2906</FONT>    <a name="line.2906"></a>
<FONT color="green">2907</FONT>          // Do one round of Newton's method in extended precision to get the last bit right.<a name="line.2907"></a>
<FONT color="green">2908</FONT>          double temp = est * HEX_40000000;<a name="line.2908"></a>
<FONT color="green">2909</FONT>          double ya = est + temp - temp;<a name="line.2909"></a>
<FONT color="green">2910</FONT>          double yb = est - ya;<a name="line.2910"></a>
<FONT color="green">2911</FONT>    <a name="line.2911"></a>
<FONT color="green">2912</FONT>          double za = ya * ya;<a name="line.2912"></a>
<FONT color="green">2913</FONT>          double zb = ya * yb * 2.0 + yb * yb;<a name="line.2913"></a>
<FONT color="green">2914</FONT>          temp = za * HEX_40000000;<a name="line.2914"></a>
<FONT color="green">2915</FONT>          double temp2 = za + temp - temp;<a name="line.2915"></a>
<FONT color="green">2916</FONT>          zb += za - temp2;<a name="line.2916"></a>
<FONT color="green">2917</FONT>          za = temp2;<a name="line.2917"></a>
<FONT color="green">2918</FONT>    <a name="line.2918"></a>
<FONT color="green">2919</FONT>          zb = za * yb + ya * zb + zb * yb;<a name="line.2919"></a>
<FONT color="green">2920</FONT>          za = za * ya;<a name="line.2920"></a>
<FONT color="green">2921</FONT>    <a name="line.2921"></a>
<FONT color="green">2922</FONT>          double na = xs - za;<a name="line.2922"></a>
<FONT color="green">2923</FONT>          double nb = -(na - xs + za);<a name="line.2923"></a>
<FONT color="green">2924</FONT>          nb -= zb;<a name="line.2924"></a>
<FONT color="green">2925</FONT>    <a name="line.2925"></a>
<FONT color="green">2926</FONT>          est += (na+nb)/(3*est*est);<a name="line.2926"></a>
<FONT color="green">2927</FONT>    <a name="line.2927"></a>
<FONT color="green">2928</FONT>          /* Scale by a power of two, so this is exact. */<a name="line.2928"></a>
<FONT color="green">2929</FONT>          est *= p2;<a name="line.2929"></a>
<FONT color="green">2930</FONT>    <a name="line.2930"></a>
<FONT color="green">2931</FONT>          if (subnormal) {<a name="line.2931"></a>
<FONT color="green">2932</FONT>              est *= 3.814697265625E-6;  // 2^-18<a name="line.2932"></a>
<FONT color="green">2933</FONT>          }<a name="line.2933"></a>
<FONT color="green">2934</FONT>    <a name="line.2934"></a>
<FONT color="green">2935</FONT>          return est;<a name="line.2935"></a>
<FONT color="green">2936</FONT>        }<a name="line.2936"></a>
<FONT color="green">2937</FONT>    <a name="line.2937"></a>
<FONT color="green">2938</FONT>        /**<a name="line.2938"></a>
<FONT color="green">2939</FONT>         *  Convert degrees to radians, with error of less than 0.5 ULP<a name="line.2939"></a>
<FONT color="green">2940</FONT>         *  @param x angle in degrees<a name="line.2940"></a>
<FONT color="green">2941</FONT>         *  @return x converted into radians<a name="line.2941"></a>
<FONT color="green">2942</FONT>         */<a name="line.2942"></a>
<FONT color="green">2943</FONT>        public static double toRadians(double x)<a name="line.2943"></a>
<FONT color="green">2944</FONT>        {<a name="line.2944"></a>
<FONT color="green">2945</FONT>            if (Double.isInfinite(x) || x == 0.0) { // Matches +/- 0.0; return correct sign<a name="line.2945"></a>
<FONT color="green">2946</FONT>                return x;<a name="line.2946"></a>
<FONT color="green">2947</FONT>            }<a name="line.2947"></a>
<FONT color="green">2948</FONT>    <a name="line.2948"></a>
<FONT color="green">2949</FONT>            // These are PI/180 split into high and low order bits<a name="line.2949"></a>
<FONT color="green">2950</FONT>            final double facta = 0.01745329052209854;<a name="line.2950"></a>
<FONT color="green">2951</FONT>            final double factb = 1.997844754509471E-9;<a name="line.2951"></a>
<FONT color="green">2952</FONT>    <a name="line.2952"></a>
<FONT color="green">2953</FONT>            double xa = doubleHighPart(x);<a name="line.2953"></a>
<FONT color="green">2954</FONT>            double xb = x - xa;<a name="line.2954"></a>
<FONT color="green">2955</FONT>    <a name="line.2955"></a>
<FONT color="green">2956</FONT>            double result = xb * factb + xb * facta + xa * factb + xa * facta;<a name="line.2956"></a>
<FONT color="green">2957</FONT>            if (result == 0) {<a name="line.2957"></a>
<FONT color="green">2958</FONT>                result = result * x; // ensure correct sign if calculation underflows<a name="line.2958"></a>
<FONT color="green">2959</FONT>            }<a name="line.2959"></a>
<FONT color="green">2960</FONT>            return result;<a name="line.2960"></a>
<FONT color="green">2961</FONT>        }<a name="line.2961"></a>
<FONT color="green">2962</FONT>    <a name="line.2962"></a>
<FONT color="green">2963</FONT>        /**<a name="line.2963"></a>
<FONT color="green">2964</FONT>         *  Convert radians to degrees, with error of less than 0.5 ULP<a name="line.2964"></a>
<FONT color="green">2965</FONT>         *  @param x angle in radians<a name="line.2965"></a>
<FONT color="green">2966</FONT>         *  @return x converted into degrees<a name="line.2966"></a>
<FONT color="green">2967</FONT>         */<a name="line.2967"></a>
<FONT color="green">2968</FONT>        public static double toDegrees(double x)<a name="line.2968"></a>
<FONT color="green">2969</FONT>        {<a name="line.2969"></a>
<FONT color="green">2970</FONT>            if (Double.isInfinite(x) || x == 0.0) { // Matches +/- 0.0; return correct sign<a name="line.2970"></a>
<FONT color="green">2971</FONT>                return x;<a name="line.2971"></a>
<FONT color="green">2972</FONT>            }<a name="line.2972"></a>
<FONT color="green">2973</FONT>    <a name="line.2973"></a>
<FONT color="green">2974</FONT>            // These are 180/PI split into high and low order bits<a name="line.2974"></a>
<FONT color="green">2975</FONT>            final double facta = 57.2957763671875;<a name="line.2975"></a>
<FONT color="green">2976</FONT>            final double factb = 3.145894820876798E-6;<a name="line.2976"></a>
<FONT color="green">2977</FONT>    <a name="line.2977"></a>
<FONT color="green">2978</FONT>            double xa = doubleHighPart(x);<a name="line.2978"></a>
<FONT color="green">2979</FONT>            double xb = x - xa;<a name="line.2979"></a>
<FONT color="green">2980</FONT>    <a name="line.2980"></a>
<FONT color="green">2981</FONT>            return xb * factb + xb * facta + xa * factb + xa * facta;<a name="line.2981"></a>
<FONT color="green">2982</FONT>        }<a name="line.2982"></a>
<FONT color="green">2983</FONT>    <a name="line.2983"></a>
<FONT color="green">2984</FONT>        /**<a name="line.2984"></a>
<FONT color="green">2985</FONT>         * Absolute value.<a name="line.2985"></a>
<FONT color="green">2986</FONT>         * @param x number from which absolute value is requested<a name="line.2986"></a>
<FONT color="green">2987</FONT>         * @return abs(x)<a name="line.2987"></a>
<FONT color="green">2988</FONT>         */<a name="line.2988"></a>
<FONT color="green">2989</FONT>        public static int abs(final int x) {<a name="line.2989"></a>
<FONT color="green">2990</FONT>            return (x &lt; 0) ? -x : x;<a name="line.2990"></a>
<FONT color="green">2991</FONT>        }<a name="line.2991"></a>
<FONT color="green">2992</FONT>    <a name="line.2992"></a>
<FONT color="green">2993</FONT>        /**<a name="line.2993"></a>
<FONT color="green">2994</FONT>         * Absolute value.<a name="line.2994"></a>
<FONT color="green">2995</FONT>         * @param x number from which absolute value is requested<a name="line.2995"></a>
<FONT color="green">2996</FONT>         * @return abs(x)<a name="line.2996"></a>
<FONT color="green">2997</FONT>         */<a name="line.2997"></a>
<FONT color="green">2998</FONT>        public static long abs(final long x) {<a name="line.2998"></a>
<FONT color="green">2999</FONT>            return (x &lt; 0l) ? -x : x;<a name="line.2999"></a>
<FONT color="green">3000</FONT>        }<a name="line.3000"></a>
<FONT color="green">3001</FONT>    <a name="line.3001"></a>
<FONT color="green">3002</FONT>        /**<a name="line.3002"></a>
<FONT color="green">3003</FONT>         * Absolute value.<a name="line.3003"></a>
<FONT color="green">3004</FONT>         * @param x number from which absolute value is requested<a name="line.3004"></a>
<FONT color="green">3005</FONT>         * @return abs(x)<a name="line.3005"></a>
<FONT color="green">3006</FONT>         */<a name="line.3006"></a>
<FONT color="green">3007</FONT>        public static float abs(final float x) {<a name="line.3007"></a>
<FONT color="green">3008</FONT>            return (x &lt; 0.0f) ? -x : (x == 0.0f) ? 0.0f : x; // -0.0 =&gt; +0.0<a name="line.3008"></a>
<FONT color="green">3009</FONT>        }<a name="line.3009"></a>
<FONT color="green">3010</FONT>    <a name="line.3010"></a>
<FONT color="green">3011</FONT>        /**<a name="line.3011"></a>
<FONT color="green">3012</FONT>         * Absolute value.<a name="line.3012"></a>
<FONT color="green">3013</FONT>         * @param x number from which absolute value is requested<a name="line.3013"></a>
<FONT color="green">3014</FONT>         * @return abs(x)<a name="line.3014"></a>
<FONT color="green">3015</FONT>         */<a name="line.3015"></a>
<FONT color="green">3016</FONT>        public static double abs(double x) {<a name="line.3016"></a>
<FONT color="green">3017</FONT>            return (x &lt; 0.0) ? -x : (x == 0.0) ? 0.0 : x; // -0.0 =&gt; +0.0<a name="line.3017"></a>
<FONT color="green">3018</FONT>        }<a name="line.3018"></a>
<FONT color="green">3019</FONT>    <a name="line.3019"></a>
<FONT color="green">3020</FONT>        /**<a name="line.3020"></a>
<FONT color="green">3021</FONT>         * Compute least significant bit (Unit in Last Position) for a number.<a name="line.3021"></a>
<FONT color="green">3022</FONT>         * @param x number from which ulp is requested<a name="line.3022"></a>
<FONT color="green">3023</FONT>         * @return ulp(x)<a name="line.3023"></a>
<FONT color="green">3024</FONT>         */<a name="line.3024"></a>
<FONT color="green">3025</FONT>        public static double ulp(double x) {<a name="line.3025"></a>
<FONT color="green">3026</FONT>            if (Double.isInfinite(x)) {<a name="line.3026"></a>
<FONT color="green">3027</FONT>                return Double.POSITIVE_INFINITY;<a name="line.3027"></a>
<FONT color="green">3028</FONT>            }<a name="line.3028"></a>
<FONT color="green">3029</FONT>            return abs(x - Double.longBitsToDouble(Double.doubleToLongBits(x) ^ 1));<a name="line.3029"></a>
<FONT color="green">3030</FONT>        }<a name="line.3030"></a>
<FONT color="green">3031</FONT>    <a name="line.3031"></a>
<FONT color="green">3032</FONT>        /**<a name="line.3032"></a>
<FONT color="green">3033</FONT>         * Compute least significant bit (Unit in Last Position) for a number.<a name="line.3033"></a>
<FONT color="green">3034</FONT>         * @param x number from which ulp is requested<a name="line.3034"></a>
<FONT color="green">3035</FONT>         * @return ulp(x)<a name="line.3035"></a>
<FONT color="green">3036</FONT>         */<a name="line.3036"></a>
<FONT color="green">3037</FONT>        public static float ulp(float x) {<a name="line.3037"></a>
<FONT color="green">3038</FONT>            if (Float.isInfinite(x)) {<a name="line.3038"></a>
<FONT color="green">3039</FONT>                return Float.POSITIVE_INFINITY;<a name="line.3039"></a>
<FONT color="green">3040</FONT>            }<a name="line.3040"></a>
<FONT color="green">3041</FONT>            return abs(x - Float.intBitsToFloat(Float.floatToIntBits(x) ^ 1));<a name="line.3041"></a>
<FONT color="green">3042</FONT>        }<a name="line.3042"></a>
<FONT color="green">3043</FONT>    <a name="line.3043"></a>
<FONT color="green">3044</FONT>        /**<a name="line.3044"></a>
<FONT color="green">3045</FONT>         * Multiply a double number by a power of 2.<a name="line.3045"></a>
<FONT color="green">3046</FONT>         * @param d number to multiply<a name="line.3046"></a>
<FONT color="green">3047</FONT>         * @param n power of 2<a name="line.3047"></a>
<FONT color="green">3048</FONT>         * @return d &amp;times; 2&lt;sup&gt;n&lt;/sup&gt;<a name="line.3048"></a>
<FONT color="green">3049</FONT>         */<a name="line.3049"></a>
<FONT color="green">3050</FONT>        public static double scalb(final double d, final int n) {<a name="line.3050"></a>
<FONT color="green">3051</FONT>    <a name="line.3051"></a>
<FONT color="green">3052</FONT>            // first simple and fast handling when 2^n can be represented using normal numbers<a name="line.3052"></a>
<FONT color="green">3053</FONT>            if ((n &gt; -1023) &amp;&amp; (n &lt; 1024)) {<a name="line.3053"></a>
<FONT color="green">3054</FONT>                return d * Double.longBitsToDouble(((long) (n + 1023)) &lt;&lt; 52);<a name="line.3054"></a>
<FONT color="green">3055</FONT>            }<a name="line.3055"></a>
<FONT color="green">3056</FONT>    <a name="line.3056"></a>
<FONT color="green">3057</FONT>            // handle special cases<a name="line.3057"></a>
<FONT color="green">3058</FONT>            if (Double.isNaN(d) || Double.isInfinite(d) || (d == 0)) {<a name="line.3058"></a>
<FONT color="green">3059</FONT>                return d;<a name="line.3059"></a>
<FONT color="green">3060</FONT>            }<a name="line.3060"></a>
<FONT color="green">3061</FONT>            if (n &lt; -2098) {<a name="line.3061"></a>
<FONT color="green">3062</FONT>                return (d &gt; 0) ? 0.0 : -0.0;<a name="line.3062"></a>
<FONT color="green">3063</FONT>            }<a name="line.3063"></a>
<FONT color="green">3064</FONT>            if (n &gt; 2097) {<a name="line.3064"></a>
<FONT color="green">3065</FONT>                return (d &gt; 0) ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;<a name="line.3065"></a>
<FONT color="green">3066</FONT>            }<a name="line.3066"></a>
<FONT color="green">3067</FONT>    <a name="line.3067"></a>
<FONT color="green">3068</FONT>            // decompose d<a name="line.3068"></a>
<FONT color="green">3069</FONT>            final long bits = Double.doubleToLongBits(d);<a name="line.3069"></a>
<FONT color="green">3070</FONT>            final long sign = bits &amp; 0x8000000000000000L;<a name="line.3070"></a>
<FONT color="green">3071</FONT>            int  exponent   = ((int) (bits &gt;&gt;&gt; 52)) &amp; 0x7ff;<a name="line.3071"></a>
<FONT color="green">3072</FONT>            long mantissa   = bits &amp; 0x000fffffffffffffL;<a name="line.3072"></a>
<FONT color="green">3073</FONT>    <a name="line.3073"></a>
<FONT color="green">3074</FONT>            // compute scaled exponent<a name="line.3074"></a>
<FONT color="green">3075</FONT>            int scaledExponent = exponent + n;<a name="line.3075"></a>
<FONT color="green">3076</FONT>    <a name="line.3076"></a>
<FONT color="green">3077</FONT>            if (n &lt; 0) {<a name="line.3077"></a>
<FONT color="green">3078</FONT>                // we are really in the case n &lt;= -1023<a name="line.3078"></a>
<FONT color="green">3079</FONT>                if (scaledExponent &gt; 0) {<a name="line.3079"></a>
<FONT color="green">3080</FONT>                    // both the input and the result are normal numbers, we only adjust the exponent<a name="line.3080"></a>
<FONT color="green">3081</FONT>                    return Double.longBitsToDouble(sign | (((long) scaledExponent) &lt;&lt; 52) | mantissa);<a name="line.3081"></a>
<FONT color="green">3082</FONT>                } else if (scaledExponent &gt; -53) {<a name="line.3082"></a>
<FONT color="green">3083</FONT>                    // the input is a normal number and the result is a subnormal number<a name="line.3083"></a>
<FONT color="green">3084</FONT>    <a name="line.3084"></a>
<FONT color="green">3085</FONT>                    // recover the hidden mantissa bit<a name="line.3085"></a>
<FONT color="green">3086</FONT>                    mantissa = mantissa | (1L &lt;&lt; 52);<a name="line.3086"></a>
<FONT color="green">3087</FONT>    <a name="line.3087"></a>
<FONT color="green">3088</FONT>                    // scales down complete mantissa, hence losing least significant bits<a name="line.3088"></a>
<FONT color="green">3089</FONT>                    final long mostSignificantLostBit = mantissa &amp; (1L &lt;&lt; (-scaledExponent));<a name="line.3089"></a>
<FONT color="green">3090</FONT>                    mantissa = mantissa &gt;&gt;&gt; (1 - scaledExponent);<a name="line.3090"></a>
<FONT color="green">3091</FONT>                    if (mostSignificantLostBit != 0) {<a name="line.3091"></a>
<FONT color="green">3092</FONT>                        // we need to add 1 bit to round up the result<a name="line.3092"></a>
<FONT color="green">3093</FONT>                        mantissa++;<a name="line.3093"></a>
<FONT color="green">3094</FONT>                    }<a name="line.3094"></a>
<FONT color="green">3095</FONT>                    return Double.longBitsToDouble(sign | mantissa);<a name="line.3095"></a>
<FONT color="green">3096</FONT>    <a name="line.3096"></a>
<FONT color="green">3097</FONT>                } else {<a name="line.3097"></a>
<FONT color="green">3098</FONT>                    // no need to compute the mantissa, the number scales down to 0<a name="line.3098"></a>
<FONT color="green">3099</FONT>                    return (sign == 0L) ? 0.0 : -0.0;<a name="line.3099"></a>
<FONT color="green">3100</FONT>                }<a name="line.3100"></a>
<FONT color="green">3101</FONT>            } else {<a name="line.3101"></a>
<FONT color="green">3102</FONT>                // we are really in the case n &gt;= 1024<a name="line.3102"></a>
<FONT color="green">3103</FONT>                if (exponent == 0) {<a name="line.3103"></a>
<FONT color="green">3104</FONT>    <a name="line.3104"></a>
<FONT color="green">3105</FONT>                    // the input number is subnormal, normalize it<a name="line.3105"></a>
<FONT color="green">3106</FONT>                    while ((mantissa &gt;&gt;&gt; 52) != 1) {<a name="line.3106"></a>
<FONT color="green">3107</FONT>                        mantissa = mantissa &lt;&lt; 1;<a name="line.3107"></a>
<FONT color="green">3108</FONT>                        --scaledExponent;<a name="line.3108"></a>
<FONT color="green">3109</FONT>                    }<a name="line.3109"></a>
<FONT color="green">3110</FONT>                    ++scaledExponent;<a name="line.3110"></a>
<FONT color="green">3111</FONT>                    mantissa = mantissa &amp; 0x000fffffffffffffL;<a name="line.3111"></a>
<FONT color="green">3112</FONT>    <a name="line.3112"></a>
<FONT color="green">3113</FONT>                    if (scaledExponent &lt; 2047) {<a name="line.3113"></a>
<FONT color="green">3114</FONT>                        return Double.longBitsToDouble(sign | (((long) scaledExponent) &lt;&lt; 52) | mantissa);<a name="line.3114"></a>
<FONT color="green">3115</FONT>                    } else {<a name="line.3115"></a>
<FONT color="green">3116</FONT>                        return (sign == 0L) ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;<a name="line.3116"></a>
<FONT color="green">3117</FONT>                    }<a name="line.3117"></a>
<FONT color="green">3118</FONT>    <a name="line.3118"></a>
<FONT color="green">3119</FONT>                } else if (scaledExponent &lt; 2047) {<a name="line.3119"></a>
<FONT color="green">3120</FONT>                    return Double.longBitsToDouble(sign | (((long) scaledExponent) &lt;&lt; 52) | mantissa);<a name="line.3120"></a>
<FONT color="green">3121</FONT>                } else {<a name="line.3121"></a>
<FONT color="green">3122</FONT>                    return (sign == 0L) ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;<a name="line.3122"></a>
<FONT color="green">3123</FONT>                }<a name="line.3123"></a>
<FONT color="green">3124</FONT>            }<a name="line.3124"></a>
<FONT color="green">3125</FONT>    <a name="line.3125"></a>
<FONT color="green">3126</FONT>        }<a name="line.3126"></a>
<FONT color="green">3127</FONT>    <a name="line.3127"></a>
<FONT color="green">3128</FONT>        /**<a name="line.3128"></a>
<FONT color="green">3129</FONT>         * Multiply a float number by a power of 2.<a name="line.3129"></a>
<FONT color="green">3130</FONT>         * @param f number to multiply<a name="line.3130"></a>
<FONT color="green">3131</FONT>         * @param n power of 2<a name="line.3131"></a>
<FONT color="green">3132</FONT>         * @return f &amp;times; 2&lt;sup&gt;n&lt;/sup&gt;<a name="line.3132"></a>
<FONT color="green">3133</FONT>         */<a name="line.3133"></a>
<FONT color="green">3134</FONT>        public static float scalb(final float f, final int n) {<a name="line.3134"></a>
<FONT color="green">3135</FONT>    <a name="line.3135"></a>
<FONT color="green">3136</FONT>            // first simple and fast handling when 2^n can be represented using normal numbers<a name="line.3136"></a>
<FONT color="green">3137</FONT>            if ((n &gt; -127) &amp;&amp; (n &lt; 128)) {<a name="line.3137"></a>
<FONT color="green">3138</FONT>                return f * Float.intBitsToFloat((n + 127) &lt;&lt; 23);<a name="line.3138"></a>
<FONT color="green">3139</FONT>            }<a name="line.3139"></a>
<FONT color="green">3140</FONT>    <a name="line.3140"></a>
<FONT color="green">3141</FONT>            // handle special cases<a name="line.3141"></a>
<FONT color="green">3142</FONT>            if (Float.isNaN(f) || Float.isInfinite(f) || (f == 0f)) {<a name="line.3142"></a>
<FONT color="green">3143</FONT>                return f;<a name="line.3143"></a>
<FONT color="green">3144</FONT>            }<a name="line.3144"></a>
<FONT color="green">3145</FONT>            if (n &lt; -277) {<a name="line.3145"></a>
<FONT color="green">3146</FONT>                return (f &gt; 0) ? 0.0f : -0.0f;<a name="line.3146"></a>
<FONT color="green">3147</FONT>            }<a name="line.3147"></a>
<FONT color="green">3148</FONT>            if (n &gt; 276) {<a name="line.3148"></a>
<FONT color="green">3149</FONT>                return (f &gt; 0) ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;<a name="line.3149"></a>
<FONT color="green">3150</FONT>            }<a name="line.3150"></a>
<FONT color="green">3151</FONT>    <a name="line.3151"></a>
<FONT color="green">3152</FONT>            // decompose f<a name="line.3152"></a>
<FONT color="green">3153</FONT>            final int bits = Float.floatToIntBits(f);<a name="line.3153"></a>
<FONT color="green">3154</FONT>            final int sign = bits &amp; 0x80000000;<a name="line.3154"></a>
<FONT color="green">3155</FONT>            int  exponent  = (bits &gt;&gt;&gt; 23) &amp; 0xff;<a name="line.3155"></a>
<FONT color="green">3156</FONT>            int mantissa   = bits &amp; 0x007fffff;<a name="line.3156"></a>
<FONT color="green">3157</FONT>    <a name="line.3157"></a>
<FONT color="green">3158</FONT>            // compute scaled exponent<a name="line.3158"></a>
<FONT color="green">3159</FONT>            int scaledExponent = exponent + n;<a name="line.3159"></a>
<FONT color="green">3160</FONT>    <a name="line.3160"></a>
<FONT color="green">3161</FONT>            if (n &lt; 0) {<a name="line.3161"></a>
<FONT color="green">3162</FONT>                // we are really in the case n &lt;= -127<a name="line.3162"></a>
<FONT color="green">3163</FONT>                if (scaledExponent &gt; 0) {<a name="line.3163"></a>
<FONT color="green">3164</FONT>                    // both the input and the result are normal numbers, we only adjust the exponent<a name="line.3164"></a>
<FONT color="green">3165</FONT>                    return Float.intBitsToFloat(sign | (scaledExponent &lt;&lt; 23) | mantissa);<a name="line.3165"></a>
<FONT color="green">3166</FONT>                } else if (scaledExponent &gt; -24) {<a name="line.3166"></a>
<FONT color="green">3167</FONT>                    // the input is a normal number and the result is a subnormal number<a name="line.3167"></a>
<FONT color="green">3168</FONT>    <a name="line.3168"></a>
<FONT color="green">3169</FONT>                    // recover the hidden mantissa bit<a name="line.3169"></a>
<FONT color="green">3170</FONT>                    mantissa = mantissa | (1 &lt;&lt; 23);<a name="line.3170"></a>
<FONT color="green">3171</FONT>    <a name="line.3171"></a>
<FONT color="green">3172</FONT>                    // scales down complete mantissa, hence losing least significant bits<a name="line.3172"></a>
<FONT color="green">3173</FONT>                    final int mostSignificantLostBit = mantissa &amp; (1 &lt;&lt; (-scaledExponent));<a name="line.3173"></a>
<FONT color="green">3174</FONT>                    mantissa = mantissa &gt;&gt;&gt; (1 - scaledExponent);<a name="line.3174"></a>
<FONT color="green">3175</FONT>                    if (mostSignificantLostBit != 0) {<a name="line.3175"></a>
<FONT color="green">3176</FONT>                        // we need to add 1 bit to round up the result<a name="line.3176"></a>
<FONT color="green">3177</FONT>                        mantissa++;<a name="line.3177"></a>
<FONT color="green">3178</FONT>                    }<a name="line.3178"></a>
<FONT color="green">3179</FONT>                    return Float.intBitsToFloat(sign | mantissa);<a name="line.3179"></a>
<FONT color="green">3180</FONT>    <a name="line.3180"></a>
<FONT color="green">3181</FONT>                } else {<a name="line.3181"></a>
<FONT color="green">3182</FONT>                    // no need to compute the mantissa, the number scales down to 0<a name="line.3182"></a>
<FONT color="green">3183</FONT>                    return (sign == 0) ? 0.0f : -0.0f;<a name="line.3183"></a>
<FONT color="green">3184</FONT>                }<a name="line.3184"></a>
<FONT color="green">3185</FONT>            } else {<a name="line.3185"></a>
<FONT color="green">3186</FONT>                // we are really in the case n &gt;= 128<a name="line.3186"></a>
<FONT color="green">3187</FONT>                if (exponent == 0) {<a name="line.3187"></a>
<FONT color="green">3188</FONT>    <a name="line.3188"></a>
<FONT color="green">3189</FONT>                    // the input number is subnormal, normalize it<a name="line.3189"></a>
<FONT color="green">3190</FONT>                    while ((mantissa &gt;&gt;&gt; 23) != 1) {<a name="line.3190"></a>
<FONT color="green">3191</FONT>                        mantissa = mantissa &lt;&lt; 1;<a name="line.3191"></a>
<FONT color="green">3192</FONT>                        --scaledExponent;<a name="line.3192"></a>
<FONT color="green">3193</FONT>                    }<a name="line.3193"></a>
<FONT color="green">3194</FONT>                    ++scaledExponent;<a name="line.3194"></a>
<FONT color="green">3195</FONT>                    mantissa = mantissa &amp; 0x007fffff;<a name="line.3195"></a>
<FONT color="green">3196</FONT>    <a name="line.3196"></a>
<FONT color="green">3197</FONT>                    if (scaledExponent &lt; 255) {<a name="line.3197"></a>
<FONT color="green">3198</FONT>                        return Float.intBitsToFloat(sign | (scaledExponent &lt;&lt; 23) | mantissa);<a name="line.3198"></a>
<FONT color="green">3199</FONT>                    } else {<a name="line.3199"></a>
<FONT color="green">3200</FONT>                        return (sign == 0) ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;<a name="line.3200"></a>
<FONT color="green">3201</FONT>                    }<a name="line.3201"></a>
<FONT color="green">3202</FONT>    <a name="line.3202"></a>
<FONT color="green">3203</FONT>                } else if (scaledExponent &lt; 255) {<a name="line.3203"></a>
<FONT color="green">3204</FONT>                    return Float.intBitsToFloat(sign | (scaledExponent &lt;&lt; 23) | mantissa);<a name="line.3204"></a>
<FONT color="green">3205</FONT>                } else {<a name="line.3205"></a>
<FONT color="green">3206</FONT>                    return (sign == 0) ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;<a name="line.3206"></a>
<FONT color="green">3207</FONT>                }<a name="line.3207"></a>
<FONT color="green">3208</FONT>            }<a name="line.3208"></a>
<FONT color="green">3209</FONT>    <a name="line.3209"></a>
<FONT color="green">3210</FONT>        }<a name="line.3210"></a>
<FONT color="green">3211</FONT>    <a name="line.3211"></a>
<FONT color="green">3212</FONT>        /**<a name="line.3212"></a>
<FONT color="green">3213</FONT>         * Get the next machine representable number after a number, moving<a name="line.3213"></a>
<FONT color="green">3214</FONT>         * in the direction of another number.<a name="line.3214"></a>
<FONT color="green">3215</FONT>         * &lt;p&gt;<a name="line.3215"></a>
<FONT color="green">3216</FONT>         * The ordering is as follows (increasing):<a name="line.3216"></a>
<FONT color="green">3217</FONT>         * &lt;ul&gt;<a name="line.3217"></a>
<FONT color="green">3218</FONT>         * &lt;li&gt;-INFINITY&lt;/li&gt;<a name="line.3218"></a>
<FONT color="green">3219</FONT>         * &lt;li&gt;-MAX_VALUE&lt;/li&gt;<a name="line.3219"></a>
<FONT color="green">3220</FONT>         * &lt;li&gt;-MIN_VALUE&lt;/li&gt;<a name="line.3220"></a>
<FONT color="green">3221</FONT>         * &lt;li&gt;-0.0&lt;/li&gt;<a name="line.3221"></a>
<FONT color="green">3222</FONT>         * &lt;li&gt;+0.0&lt;/li&gt;<a name="line.3222"></a>
<FONT color="green">3223</FONT>         * &lt;li&gt;+MIN_VALUE&lt;/li&gt;<a name="line.3223"></a>
<FONT color="green">3224</FONT>         * &lt;li&gt;+MAX_VALUE&lt;/li&gt;<a name="line.3224"></a>
<FONT color="green">3225</FONT>         * &lt;li&gt;+INFINITY&lt;/li&gt;<a name="line.3225"></a>
<FONT color="green">3226</FONT>         * &lt;li&gt;&lt;/li&gt;<a name="line.3226"></a>
<FONT color="green">3227</FONT>         * &lt;p&gt;<a name="line.3227"></a>
<FONT color="green">3228</FONT>         * If arguments compare equal, then the second argument is returned.<a name="line.3228"></a>
<FONT color="green">3229</FONT>         * &lt;p&gt;<a name="line.3229"></a>
<FONT color="green">3230</FONT>         * If {@code direction} is greater than {@code d},<a name="line.3230"></a>
<FONT color="green">3231</FONT>         * the smallest machine representable number strictly greater than<a name="line.3231"></a>
<FONT color="green">3232</FONT>         * {@code d} is returned; if less, then the largest representable number<a name="line.3232"></a>
<FONT color="green">3233</FONT>         * strictly less than {@code d} is returned.&lt;/p&gt;<a name="line.3233"></a>
<FONT color="green">3234</FONT>         * &lt;p&gt;<a name="line.3234"></a>
<FONT color="green">3235</FONT>         * If {@code d} is infinite and direction does not<a name="line.3235"></a>
<FONT color="green">3236</FONT>         * bring it back to finite numbers, it is returned unchanged.&lt;/p&gt;<a name="line.3236"></a>
<FONT color="green">3237</FONT>         *<a name="line.3237"></a>
<FONT color="green">3238</FONT>         * @param d base number<a name="line.3238"></a>
<FONT color="green">3239</FONT>         * @param direction (the only important thing is whether<a name="line.3239"></a>
<FONT color="green">3240</FONT>         * {@code direction} is greater or smaller than {@code d})<a name="line.3240"></a>
<FONT color="green">3241</FONT>         * @return the next machine representable number in the specified direction<a name="line.3241"></a>
<FONT color="green">3242</FONT>         */<a name="line.3242"></a>
<FONT color="green">3243</FONT>        public static double nextAfter(double d, double direction) {<a name="line.3243"></a>
<FONT color="green">3244</FONT>    <a name="line.3244"></a>
<FONT color="green">3245</FONT>            // handling of some important special cases<a name="line.3245"></a>
<FONT color="green">3246</FONT>            if (Double.isNaN(d) || Double.isNaN(direction)) {<a name="line.3246"></a>
<FONT color="green">3247</FONT>                return Double.NaN;<a name="line.3247"></a>
<FONT color="green">3248</FONT>            } else if (d == direction) {<a name="line.3248"></a>
<FONT color="green">3249</FONT>                return direction;<a name="line.3249"></a>
<FONT color="green">3250</FONT>            } else if (Double.isInfinite(d)) {<a name="line.3250"></a>
<FONT color="green">3251</FONT>                return (d &lt; 0) ? -Double.MAX_VALUE : Double.MAX_VALUE;<a name="line.3251"></a>
<FONT color="green">3252</FONT>            } else if (d == 0) {<a name="line.3252"></a>
<FONT color="green">3253</FONT>                return (direction &lt; 0) ? -Double.MIN_VALUE : Double.MIN_VALUE;<a name="line.3253"></a>
<FONT color="green">3254</FONT>            }<a name="line.3254"></a>
<FONT color="green">3255</FONT>            // special cases MAX_VALUE to infinity and  MIN_VALUE to 0<a name="line.3255"></a>
<FONT color="green">3256</FONT>            // are handled just as normal numbers<a name="line.3256"></a>
<FONT color="green">3257</FONT>    <a name="line.3257"></a>
<FONT color="green">3258</FONT>            final long bits = Double.doubleToLongBits(d);<a name="line.3258"></a>
<FONT color="green">3259</FONT>            final long sign = bits &amp; 0x8000000000000000L;<a name="line.3259"></a>
<FONT color="green">3260</FONT>            if ((direction &lt; d) ^ (sign == 0L)) {<a name="line.3260"></a>
<FONT color="green">3261</FONT>                return Double.longBitsToDouble(sign | ((bits &amp; 0x7fffffffffffffffL) + 1));<a name="line.3261"></a>
<FONT color="green">3262</FONT>            } else {<a name="line.3262"></a>
<FONT color="green">3263</FONT>                return Double.longBitsToDouble(sign | ((bits &amp; 0x7fffffffffffffffL) - 1));<a name="line.3263"></a>
<FONT color="green">3264</FONT>            }<a name="line.3264"></a>
<FONT color="green">3265</FONT>    <a name="line.3265"></a>
<FONT color="green">3266</FONT>        }<a name="line.3266"></a>
<FONT color="green">3267</FONT>    <a name="line.3267"></a>
<FONT color="green">3268</FONT>        /**<a name="line.3268"></a>
<FONT color="green">3269</FONT>         * Get the next machine representable number after a number, moving<a name="line.3269"></a>
<FONT color="green">3270</FONT>         * in the direction of another number.<a name="line.3270"></a>
<FONT color="green">3271</FONT>         * &lt;p&gt;<a name="line.3271"></a>
<FONT color="green">3272</FONT>         * The ordering is as follows (increasing):<a name="line.3272"></a>
<FONT color="green">3273</FONT>         * &lt;ul&gt;<a name="line.3273"></a>
<FONT color="green">3274</FONT>         * &lt;li&gt;-INFINITY&lt;/li&gt;<a name="line.3274"></a>
<FONT color="green">3275</FONT>         * &lt;li&gt;-MAX_VALUE&lt;/li&gt;<a name="line.3275"></a>
<FONT color="green">3276</FONT>         * &lt;li&gt;-MIN_VALUE&lt;/li&gt;<a name="line.3276"></a>
<FONT color="green">3277</FONT>         * &lt;li&gt;-0.0&lt;/li&gt;<a name="line.3277"></a>
<FONT color="green">3278</FONT>         * &lt;li&gt;+0.0&lt;/li&gt;<a name="line.3278"></a>
<FONT color="green">3279</FONT>         * &lt;li&gt;+MIN_VALUE&lt;/li&gt;<a name="line.3279"></a>
<FONT color="green">3280</FONT>         * &lt;li&gt;+MAX_VALUE&lt;/li&gt;<a name="line.3280"></a>
<FONT color="green">3281</FONT>         * &lt;li&gt;+INFINITY&lt;/li&gt;<a name="line.3281"></a>
<FONT color="green">3282</FONT>         * &lt;li&gt;&lt;/li&gt;<a name="line.3282"></a>
<FONT color="green">3283</FONT>         * &lt;p&gt;<a name="line.3283"></a>
<FONT color="green">3284</FONT>         * If arguments compare equal, then the second argument is returned.<a name="line.3284"></a>
<FONT color="green">3285</FONT>         * &lt;p&gt;<a name="line.3285"></a>
<FONT color="green">3286</FONT>         * If {@code direction} is greater than {@code f},<a name="line.3286"></a>
<FONT color="green">3287</FONT>         * the smallest machine representable number strictly greater than<a name="line.3287"></a>
<FONT color="green">3288</FONT>         * {@code f} is returned; if less, then the largest representable number<a name="line.3288"></a>
<FONT color="green">3289</FONT>         * strictly less than {@code f} is returned.&lt;/p&gt;<a name="line.3289"></a>
<FONT color="green">3290</FONT>         * &lt;p&gt;<a name="line.3290"></a>
<FONT color="green">3291</FONT>         * If {@code f} is infinite and direction does not<a name="line.3291"></a>
<FONT color="green">3292</FONT>         * bring it back to finite numbers, it is returned unchanged.&lt;/p&gt;<a name="line.3292"></a>
<FONT color="green">3293</FONT>         *<a name="line.3293"></a>
<FONT color="green">3294</FONT>         * @param f base number<a name="line.3294"></a>
<FONT color="green">3295</FONT>         * @param direction (the only important thing is whether<a name="line.3295"></a>
<FONT color="green">3296</FONT>         * {@code direction} is greater or smaller than {@code f})<a name="line.3296"></a>
<FONT color="green">3297</FONT>         * @return the next machine representable number in the specified direction<a name="line.3297"></a>
<FONT color="green">3298</FONT>         */<a name="line.3298"></a>
<FONT color="green">3299</FONT>        public static float nextAfter(final float f, final double direction) {<a name="line.3299"></a>
<FONT color="green">3300</FONT>    <a name="line.3300"></a>
<FONT color="green">3301</FONT>            // handling of some important special cases<a name="line.3301"></a>
<FONT color="green">3302</FONT>            if (Double.isNaN(f) || Double.isNaN(direction)) {<a name="line.3302"></a>
<FONT color="green">3303</FONT>                return Float.NaN;<a name="line.3303"></a>
<FONT color="green">3304</FONT>            } else if (f == direction) {<a name="line.3304"></a>
<FONT color="green">3305</FONT>                return (float) direction;<a name="line.3305"></a>
<FONT color="green">3306</FONT>            } else if (Float.isInfinite(f)) {<a name="line.3306"></a>
<FONT color="green">3307</FONT>                return (f &lt; 0f) ? -Float.MAX_VALUE : Float.MAX_VALUE;<a name="line.3307"></a>
<FONT color="green">3308</FONT>            } else if (f == 0f) {<a name="line.3308"></a>
<FONT color="green">3309</FONT>                return (direction &lt; 0) ? -Float.MIN_VALUE : Float.MIN_VALUE;<a name="line.3309"></a>
<FONT color="green">3310</FONT>            }<a name="line.3310"></a>
<FONT color="green">3311</FONT>            // special cases MAX_VALUE to infinity and  MIN_VALUE to 0<a name="line.3311"></a>
<FONT color="green">3312</FONT>            // are handled just as normal numbers<a name="line.3312"></a>
<FONT color="green">3313</FONT>    <a name="line.3313"></a>
<FONT color="green">3314</FONT>            final int bits = Float.floatToIntBits(f);<a name="line.3314"></a>
<FONT color="green">3315</FONT>            final int sign = bits &amp; 0x80000000;<a name="line.3315"></a>
<FONT color="green">3316</FONT>            if ((direction &lt; f) ^ (sign == 0)) {<a name="line.3316"></a>
<FONT color="green">3317</FONT>                return Float.intBitsToFloat(sign | ((bits &amp; 0x7fffffff) + 1));<a name="line.3317"></a>
<FONT color="green">3318</FONT>            } else {<a name="line.3318"></a>
<FONT color="green">3319</FONT>                return Float.intBitsToFloat(sign | ((bits &amp; 0x7fffffff) - 1));<a name="line.3319"></a>
<FONT color="green">3320</FONT>            }<a name="line.3320"></a>
<FONT color="green">3321</FONT>    <a name="line.3321"></a>
<FONT color="green">3322</FONT>        }<a name="line.3322"></a>
<FONT color="green">3323</FONT>    <a name="line.3323"></a>
<FONT color="green">3324</FONT>        /** Get the largest whole number smaller than x.<a name="line.3324"></a>
<FONT color="green">3325</FONT>         * @param x number from which floor is requested<a name="line.3325"></a>
<FONT color="green">3326</FONT>         * @return a double number f such that f is an integer f &lt;= x &lt; f + 1.0<a name="line.3326"></a>
<FONT color="green">3327</FONT>         */<a name="line.3327"></a>
<FONT color="green">3328</FONT>        public static double floor(double x) {<a name="line.3328"></a>
<FONT color="green">3329</FONT>            long y;<a name="line.3329"></a>
<FONT color="green">3330</FONT>    <a name="line.3330"></a>
<FONT color="green">3331</FONT>            if (x != x) { // NaN<a name="line.3331"></a>
<FONT color="green">3332</FONT>                return x;<a name="line.3332"></a>
<FONT color="green">3333</FONT>            }<a name="line.3333"></a>
<FONT color="green">3334</FONT>    <a name="line.3334"></a>
<FONT color="green">3335</FONT>            if (x &gt;= TWO_POWER_52 || x &lt;= -TWO_POWER_52) {<a name="line.3335"></a>
<FONT color="green">3336</FONT>                return x;<a name="line.3336"></a>
<FONT color="green">3337</FONT>            }<a name="line.3337"></a>
<FONT color="green">3338</FONT>    <a name="line.3338"></a>
<FONT color="green">3339</FONT>            y = (long) x;<a name="line.3339"></a>
<FONT color="green">3340</FONT>            if (x &lt; 0 &amp;&amp; y != x) {<a name="line.3340"></a>
<FONT color="green">3341</FONT>                y--;<a name="line.3341"></a>
<FONT color="green">3342</FONT>            }<a name="line.3342"></a>
<FONT color="green">3343</FONT>    <a name="line.3343"></a>
<FONT color="green">3344</FONT>            if (y == 0) {<a name="line.3344"></a>
<FONT color="green">3345</FONT>                return x*y;<a name="line.3345"></a>
<FONT color="green">3346</FONT>            }<a name="line.3346"></a>
<FONT color="green">3347</FONT>    <a name="line.3347"></a>
<FONT color="green">3348</FONT>            return y;<a name="line.3348"></a>
<FONT color="green">3349</FONT>        }<a name="line.3349"></a>
<FONT color="green">3350</FONT>    <a name="line.3350"></a>
<FONT color="green">3351</FONT>        /** Get the smallest whole number larger than x.<a name="line.3351"></a>
<FONT color="green">3352</FONT>         * @param x number from which ceil is requested<a name="line.3352"></a>
<FONT color="green">3353</FONT>         * @return a double number c such that c is an integer c - 1.0 &lt; x &lt;= c<a name="line.3353"></a>
<FONT color="green">3354</FONT>         */<a name="line.3354"></a>
<FONT color="green">3355</FONT>        public static double ceil(double x) {<a name="line.3355"></a>
<FONT color="green">3356</FONT>            double y;<a name="line.3356"></a>
<FONT color="green">3357</FONT>    <a name="line.3357"></a>
<FONT color="green">3358</FONT>            if (x != x) { // NaN<a name="line.3358"></a>
<FONT color="green">3359</FONT>                return x;<a name="line.3359"></a>
<FONT color="green">3360</FONT>            }<a name="line.3360"></a>
<FONT color="green">3361</FONT>    <a name="line.3361"></a>
<FONT color="green">3362</FONT>            y = floor(x);<a name="line.3362"></a>
<FONT color="green">3363</FONT>            if (y == x) {<a name="line.3363"></a>
<FONT color="green">3364</FONT>                return y;<a name="line.3364"></a>
<FONT color="green">3365</FONT>            }<a name="line.3365"></a>
<FONT color="green">3366</FONT>    <a name="line.3366"></a>
<FONT color="green">3367</FONT>            y += 1.0;<a name="line.3367"></a>
<FONT color="green">3368</FONT>    <a name="line.3368"></a>
<FONT color="green">3369</FONT>            if (y == 0) {<a name="line.3369"></a>
<FONT color="green">3370</FONT>                return x*y;<a name="line.3370"></a>
<FONT color="green">3371</FONT>            }<a name="line.3371"></a>
<FONT color="green">3372</FONT>    <a name="line.3372"></a>
<FONT color="green">3373</FONT>            return y;<a name="line.3373"></a>
<FONT color="green">3374</FONT>        }<a name="line.3374"></a>
<FONT color="green">3375</FONT>    <a name="line.3375"></a>
<FONT color="green">3376</FONT>        /** Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.<a name="line.3376"></a>
<FONT color="green">3377</FONT>         * @param x number from which nearest whole number is requested<a name="line.3377"></a>
<FONT color="green">3378</FONT>         * @return a double number r such that r is an integer r - 0.5 &lt;= x &lt;= r + 0.5<a name="line.3378"></a>
<FONT color="green">3379</FONT>         */<a name="line.3379"></a>
<FONT color="green">3380</FONT>        public static double rint(double x) {<a name="line.3380"></a>
<FONT color="green">3381</FONT>            double y = floor(x);<a name="line.3381"></a>
<FONT color="green">3382</FONT>            double d = x - y;<a name="line.3382"></a>
<FONT color="green">3383</FONT>    <a name="line.3383"></a>
<FONT color="green">3384</FONT>            if (d &gt; 0.5) {<a name="line.3384"></a>
<FONT color="green">3385</FONT>                if (y == -1.0) {<a name="line.3385"></a>
<FONT color="green">3386</FONT>                    return -0.0; // Preserve sign of operand<a name="line.3386"></a>
<FONT color="green">3387</FONT>                }<a name="line.3387"></a>
<FONT color="green">3388</FONT>                return y+1.0;<a name="line.3388"></a>
<FONT color="green">3389</FONT>            }<a name="line.3389"></a>
<FONT color="green">3390</FONT>            if (d &lt; 0.5) {<a name="line.3390"></a>
<FONT color="green">3391</FONT>                return y;<a name="line.3391"></a>
<FONT color="green">3392</FONT>            }<a name="line.3392"></a>
<FONT color="green">3393</FONT>    <a name="line.3393"></a>
<FONT color="green">3394</FONT>            /* half way, round to even */<a name="line.3394"></a>
<FONT color="green">3395</FONT>            long z = (long) y;<a name="line.3395"></a>
<FONT color="green">3396</FONT>            return (z &amp; 1) == 0 ? y : y + 1.0;<a name="line.3396"></a>
<FONT color="green">3397</FONT>        }<a name="line.3397"></a>
<FONT color="green">3398</FONT>    <a name="line.3398"></a>
<FONT color="green">3399</FONT>        /** Get the closest long to x.<a name="line.3399"></a>
<FONT color="green">3400</FONT>         * @param x number from which closest long is requested<a name="line.3400"></a>
<FONT color="green">3401</FONT>         * @return closest long to x<a name="line.3401"></a>
<FONT color="green">3402</FONT>         */<a name="line.3402"></a>
<FONT color="green">3403</FONT>        public static long round(double x) {<a name="line.3403"></a>
<FONT color="green">3404</FONT>            return (long) floor(x + 0.5);<a name="line.3404"></a>
<FONT color="green">3405</FONT>        }<a name="line.3405"></a>
<FONT color="green">3406</FONT>    <a name="line.3406"></a>
<FONT color="green">3407</FONT>        /** Get the closest int to x.<a name="line.3407"></a>
<FONT color="green">3408</FONT>         * @param x number from which closest int is requested<a name="line.3408"></a>
<FONT color="green">3409</FONT>         * @return closest int to x<a name="line.3409"></a>
<FONT color="green">3410</FONT>         */<a name="line.3410"></a>
<FONT color="green">3411</FONT>        public static int round(final float x) {<a name="line.3411"></a>
<FONT color="green">3412</FONT>            return (int) floor(x + 0.5f);<a name="line.3412"></a>
<FONT color="green">3413</FONT>        }<a name="line.3413"></a>
<FONT color="green">3414</FONT>    <a name="line.3414"></a>
<FONT color="green">3415</FONT>        /** Compute the minimum of two values<a name="line.3415"></a>
<FONT color="green">3416</FONT>         * @param a first value<a name="line.3416"></a>
<FONT color="green">3417</FONT>         * @param b second value<a name="line.3417"></a>
<FONT color="green">3418</FONT>         * @return a if a is lesser or equal to b, b otherwise<a name="line.3418"></a>
<FONT color="green">3419</FONT>         */<a name="line.3419"></a>
<FONT color="green">3420</FONT>        public static int min(final int a, final int b) {<a name="line.3420"></a>
<FONT color="green">3421</FONT>            return (a &lt;= b) ? a : b;<a name="line.3421"></a>
<FONT color="green">3422</FONT>        }<a name="line.3422"></a>
<FONT color="green">3423</FONT>    <a name="line.3423"></a>
<FONT color="green">3424</FONT>        /** Compute the minimum of two values<a name="line.3424"></a>
<FONT color="green">3425</FONT>         * @param a first value<a name="line.3425"></a>
<FONT color="green">3426</FONT>         * @param b second value<a name="line.3426"></a>
<FONT color="green">3427</FONT>         * @return a if a is lesser or equal to b, b otherwise<a name="line.3427"></a>
<FONT color="green">3428</FONT>         */<a name="line.3428"></a>
<FONT color="green">3429</FONT>        public static long min(final long a, final long b) {<a name="line.3429"></a>
<FONT color="green">3430</FONT>            return (a &lt;= b) ? a : b;<a name="line.3430"></a>
<FONT color="green">3431</FONT>        }<a name="line.3431"></a>
<FONT color="green">3432</FONT>    <a name="line.3432"></a>
<FONT color="green">3433</FONT>        /** Compute the minimum of two values<a name="line.3433"></a>
<FONT color="green">3434</FONT>         * @param a first value<a name="line.3434"></a>
<FONT color="green">3435</FONT>         * @param b second value<a name="line.3435"></a>
<FONT color="green">3436</FONT>         * @return a if a is lesser or equal to b, b otherwise<a name="line.3436"></a>
<FONT color="green">3437</FONT>         */<a name="line.3437"></a>
<FONT color="green">3438</FONT>        public static float min(final float a, final float b) {<a name="line.3438"></a>
<FONT color="green">3439</FONT>            if (a &gt; b) {<a name="line.3439"></a>
<FONT color="green">3440</FONT>                return b;<a name="line.3440"></a>
<FONT color="green">3441</FONT>            }<a name="line.3441"></a>
<FONT color="green">3442</FONT>            if (a &lt; b) {<a name="line.3442"></a>
<FONT color="green">3443</FONT>                return a;<a name="line.3443"></a>
<FONT color="green">3444</FONT>            }<a name="line.3444"></a>
<FONT color="green">3445</FONT>            /* if either arg is NaN, return NaN */<a name="line.3445"></a>
<FONT color="green">3446</FONT>            if (a != b) {<a name="line.3446"></a>
<FONT color="green">3447</FONT>                return Float.NaN;<a name="line.3447"></a>
<FONT color="green">3448</FONT>            }<a name="line.3448"></a>
<FONT color="green">3449</FONT>            /* min(+0.0,-0.0) == -0.0 */<a name="line.3449"></a>
<FONT color="green">3450</FONT>            /* 0x80000000 == Float.floatToRawIntBits(-0.0d) */<a name="line.3450"></a>
<FONT color="green">3451</FONT>            int bits = Float.floatToRawIntBits(a);<a name="line.3451"></a>
<FONT color="green">3452</FONT>            if (bits == 0x80000000) {<a name="line.3452"></a>
<FONT color="green">3453</FONT>                return a;<a name="line.3453"></a>
<FONT color="green">3454</FONT>            }<a name="line.3454"></a>
<FONT color="green">3455</FONT>            return b;<a name="line.3455"></a>
<FONT color="green">3456</FONT>        }<a name="line.3456"></a>
<FONT color="green">3457</FONT>    <a name="line.3457"></a>
<FONT color="green">3458</FONT>        /** Compute the minimum of two values<a name="line.3458"></a>
<FONT color="green">3459</FONT>         * @param a first value<a name="line.3459"></a>
<FONT color="green">3460</FONT>         * @param b second value<a name="line.3460"></a>
<FONT color="green">3461</FONT>         * @return a if a is lesser or equal to b, b otherwise<a name="line.3461"></a>
<FONT color="green">3462</FONT>         */<a name="line.3462"></a>
<FONT color="green">3463</FONT>        public static double min(final double a, final double b) {<a name="line.3463"></a>
<FONT color="green">3464</FONT>            if (a &gt; b) {<a name="line.3464"></a>
<FONT color="green">3465</FONT>                return b;<a name="line.3465"></a>
<FONT color="green">3466</FONT>            }<a name="line.3466"></a>
<FONT color="green">3467</FONT>            if (a &lt; b) {<a name="line.3467"></a>
<FONT color="green">3468</FONT>                return a;<a name="line.3468"></a>
<FONT color="green">3469</FONT>            }<a name="line.3469"></a>
<FONT color="green">3470</FONT>            /* if either arg is NaN, return NaN */<a name="line.3470"></a>
<FONT color="green">3471</FONT>            if (a != b) {<a name="line.3471"></a>
<FONT color="green">3472</FONT>                return Double.NaN;<a name="line.3472"></a>
<FONT color="green">3473</FONT>            }<a name="line.3473"></a>
<FONT color="green">3474</FONT>            /* min(+0.0,-0.0) == -0.0 */<a name="line.3474"></a>
<FONT color="green">3475</FONT>            /* 0x8000000000000000L == Double.doubleToRawLongBits(-0.0d) */<a name="line.3475"></a>
<FONT color="green">3476</FONT>            long bits = Double.doubleToRawLongBits(a);<a name="line.3476"></a>
<FONT color="green">3477</FONT>            if (bits == 0x8000000000000000L) {<a name="line.3477"></a>
<FONT color="green">3478</FONT>                return a;<a name="line.3478"></a>
<FONT color="green">3479</FONT>            }<a name="line.3479"></a>
<FONT color="green">3480</FONT>            return b;<a name="line.3480"></a>
<FONT color="green">3481</FONT>        }<a name="line.3481"></a>
<FONT color="green">3482</FONT>    <a name="line.3482"></a>
<FONT color="green">3483</FONT>        /** Compute the maximum of two values<a name="line.3483"></a>
<FONT color="green">3484</FONT>         * @param a first value<a name="line.3484"></a>
<FONT color="green">3485</FONT>         * @param b second value<a name="line.3485"></a>
<FONT color="green">3486</FONT>         * @return b if a is lesser or equal to b, a otherwise<a name="line.3486"></a>
<FONT color="green">3487</FONT>         */<a name="line.3487"></a>
<FONT color="green">3488</FONT>        public static int max(final int a, final int b) {<a name="line.3488"></a>
<FONT color="green">3489</FONT>            return (a &lt;= b) ? b : a;<a name="line.3489"></a>
<FONT color="green">3490</FONT>        }<a name="line.3490"></a>
<FONT color="green">3491</FONT>    <a name="line.3491"></a>
<FONT color="green">3492</FONT>        /** Compute the maximum of two values<a name="line.3492"></a>
<FONT color="green">3493</FONT>         * @param a first value<a name="line.3493"></a>
<FONT color="green">3494</FONT>         * @param b second value<a name="line.3494"></a>
<FONT color="green">3495</FONT>         * @return b if a is lesser or equal to b, a otherwise<a name="line.3495"></a>
<FONT color="green">3496</FONT>         */<a name="line.3496"></a>
<FONT color="green">3497</FONT>        public static long max(final long a, final long b) {<a name="line.3497"></a>
<FONT color="green">3498</FONT>            return (a &lt;= b) ? b : a;<a name="line.3498"></a>
<FONT color="green">3499</FONT>        }<a name="line.3499"></a>
<FONT color="green">3500</FONT>    <a name="line.3500"></a>
<FONT color="green">3501</FONT>        /** Compute the maximum of two values<a name="line.3501"></a>
<FONT color="green">3502</FONT>         * @param a first value<a name="line.3502"></a>
<FONT color="green">3503</FONT>         * @param b second value<a name="line.3503"></a>
<FONT color="green">3504</FONT>         * @return b if a is lesser or equal to b, a otherwise<a name="line.3504"></a>
<FONT color="green">3505</FONT>         */<a name="line.3505"></a>
<FONT color="green">3506</FONT>        public static float max(final float a, final float b) {<a name="line.3506"></a>
<FONT color="green">3507</FONT>            if (a &gt; b) {<a name="line.3507"></a>
<FONT color="green">3508</FONT>                return a;<a name="line.3508"></a>
<FONT color="green">3509</FONT>            }<a name="line.3509"></a>
<FONT color="green">3510</FONT>            if (a &lt; b) {<a name="line.3510"></a>
<FONT color="green">3511</FONT>                return b;<a name="line.3511"></a>
<FONT color="green">3512</FONT>            }<a name="line.3512"></a>
<FONT color="green">3513</FONT>            /* if either arg is NaN, return NaN */<a name="line.3513"></a>
<FONT color="green">3514</FONT>            if (a != b) {<a name="line.3514"></a>
<FONT color="green">3515</FONT>                return Float.NaN;<a name="line.3515"></a>
<FONT color="green">3516</FONT>            }<a name="line.3516"></a>
<FONT color="green">3517</FONT>            /* min(+0.0,-0.0) == -0.0 */<a name="line.3517"></a>
<FONT color="green">3518</FONT>            /* 0x80000000 == Float.floatToRawIntBits(-0.0d) */<a name="line.3518"></a>
<FONT color="green">3519</FONT>            int bits = Float.floatToRawIntBits(a);<a name="line.3519"></a>
<FONT color="green">3520</FONT>            if (bits == 0x80000000) {<a name="line.3520"></a>
<FONT color="green">3521</FONT>                return b;<a name="line.3521"></a>
<FONT color="green">3522</FONT>            }<a name="line.3522"></a>
<FONT color="green">3523</FONT>            return a;<a name="line.3523"></a>
<FONT color="green">3524</FONT>        }<a name="line.3524"></a>
<FONT color="green">3525</FONT>    <a name="line.3525"></a>
<FONT color="green">3526</FONT>        /** Compute the maximum of two values<a name="line.3526"></a>
<FONT color="green">3527</FONT>         * @param a first value<a name="line.3527"></a>
<FONT color="green">3528</FONT>         * @param b second value<a name="line.3528"></a>
<FONT color="green">3529</FONT>         * @return b if a is lesser or equal to b, a otherwise<a name="line.3529"></a>
<FONT color="green">3530</FONT>         */<a name="line.3530"></a>
<FONT color="green">3531</FONT>        public static double max(final double a, final double b) {<a name="line.3531"></a>
<FONT color="green">3532</FONT>            if (a &gt; b) {<a name="line.3532"></a>
<FONT color="green">3533</FONT>                return a;<a name="line.3533"></a>
<FONT color="green">3534</FONT>            }<a name="line.3534"></a>
<FONT color="green">3535</FONT>            if (a &lt; b) {<a name="line.3535"></a>
<FONT color="green">3536</FONT>                return b;<a name="line.3536"></a>
<FONT color="green">3537</FONT>            }<a name="line.3537"></a>
<FONT color="green">3538</FONT>            /* if either arg is NaN, return NaN */<a name="line.3538"></a>
<FONT color="green">3539</FONT>            if (a != b) {<a name="line.3539"></a>
<FONT color="green">3540</FONT>                return Double.NaN;<a name="line.3540"></a>
<FONT color="green">3541</FONT>            }<a name="line.3541"></a>
<FONT color="green">3542</FONT>            /* min(+0.0,-0.0) == -0.0 */<a name="line.3542"></a>
<FONT color="green">3543</FONT>            /* 0x8000000000000000L == Double.doubleToRawLongBits(-0.0d) */<a name="line.3543"></a>
<FONT color="green">3544</FONT>            long bits = Double.doubleToRawLongBits(a);<a name="line.3544"></a>
<FONT color="green">3545</FONT>            if (bits == 0x8000000000000000L) {<a name="line.3545"></a>
<FONT color="green">3546</FONT>                return b;<a name="line.3546"></a>
<FONT color="green">3547</FONT>            }<a name="line.3547"></a>
<FONT color="green">3548</FONT>            return a;<a name="line.3548"></a>
<FONT color="green">3549</FONT>        }<a name="line.3549"></a>
<FONT color="green">3550</FONT>    <a name="line.3550"></a>
<FONT color="green">3551</FONT>        /**<a name="line.3551"></a>
<FONT color="green">3552</FONT>         * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}<a name="line.3552"></a>
<FONT color="green">3553</FONT>         * - sqrt(&lt;i&gt;x&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;&amp;nbsp;+&lt;i&gt;y&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;)&lt;br/&gt;<a name="line.3553"></a>
<FONT color="green">3554</FONT>         * avoiding intermediate overflow or underflow.<a name="line.3554"></a>
<FONT color="green">3555</FONT>         *<a name="line.3555"></a>
<FONT color="green">3556</FONT>         * &lt;ul&gt;<a name="line.3556"></a>
<FONT color="green">3557</FONT>         * &lt;li&gt; If either argument is infinite, then the result is positive infinity.&lt;/li&gt;<a name="line.3557"></a>
<FONT color="green">3558</FONT>         * &lt;li&gt; else, if either argument is NaN then the result is NaN.&lt;/li&gt;<a name="line.3558"></a>
<FONT color="green">3559</FONT>         * &lt;/ul&gt;<a name="line.3559"></a>
<FONT color="green">3560</FONT>         *<a name="line.3560"></a>
<FONT color="green">3561</FONT>         * @param x a value<a name="line.3561"></a>
<FONT color="green">3562</FONT>         * @param y a value<a name="line.3562"></a>
<FONT color="green">3563</FONT>         * @return sqrt(&lt;i&gt;x&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;&amp;nbsp;+&lt;i&gt;y&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;)<a name="line.3563"></a>
<FONT color="green">3564</FONT>         */<a name="line.3564"></a>
<FONT color="green">3565</FONT>        public static double hypot(final double x, final double y) {<a name="line.3565"></a>
<FONT color="green">3566</FONT>            if (Double.isInfinite(x) || Double.isInfinite(y)) {<a name="line.3566"></a>
<FONT color="green">3567</FONT>                return Double.POSITIVE_INFINITY;<a name="line.3567"></a>
<FONT color="green">3568</FONT>            } else if (Double.isNaN(x) || Double.isNaN(y)) {<a name="line.3568"></a>
<FONT color="green">3569</FONT>                return Double.NaN;<a name="line.3569"></a>
<FONT color="green">3570</FONT>            } else {<a name="line.3570"></a>
<FONT color="green">3571</FONT>    <a name="line.3571"></a>
<FONT color="green">3572</FONT>                final int expX = getExponent(x);<a name="line.3572"></a>
<FONT color="green">3573</FONT>                final int expY = getExponent(y);<a name="line.3573"></a>
<FONT color="green">3574</FONT>                if (expX &gt; expY + 27) {<a name="line.3574"></a>
<FONT color="green">3575</FONT>                    // y is neglectible with respect to x<a name="line.3575"></a>
<FONT color="green">3576</FONT>                    return abs(x);<a name="line.3576"></a>
<FONT color="green">3577</FONT>                } else if (expY &gt; expX + 27) {<a name="line.3577"></a>
<FONT color="green">3578</FONT>                    // x is neglectible with respect to y<a name="line.3578"></a>
<FONT color="green">3579</FONT>                    return abs(y);<a name="line.3579"></a>
<FONT color="green">3580</FONT>                } else {<a name="line.3580"></a>
<FONT color="green">3581</FONT>    <a name="line.3581"></a>
<FONT color="green">3582</FONT>                    // find an intermediate scale to avoid both overflow and underflow<a name="line.3582"></a>
<FONT color="green">3583</FONT>                    final int middleExp = (expX + expY) / 2;<a name="line.3583"></a>
<FONT color="green">3584</FONT>    <a name="line.3584"></a>
<FONT color="green">3585</FONT>                    // scale parameters without losing precision<a name="line.3585"></a>
<FONT color="green">3586</FONT>                    final double scaledX = scalb(x, -middleExp);<a name="line.3586"></a>
<FONT color="green">3587</FONT>                    final double scaledY = scalb(y, -middleExp);<a name="line.3587"></a>
<FONT color="green">3588</FONT>    <a name="line.3588"></a>
<FONT color="green">3589</FONT>                    // compute scaled hypotenuse<a name="line.3589"></a>
<FONT color="green">3590</FONT>                    final double scaledH = sqrt(scaledX * scaledX + scaledY * scaledY);<a name="line.3590"></a>
<FONT color="green">3591</FONT>    <a name="line.3591"></a>
<FONT color="green">3592</FONT>                    // remove scaling<a name="line.3592"></a>
<FONT color="green">3593</FONT>                    return scalb(scaledH, middleExp);<a name="line.3593"></a>
<FONT color="green">3594</FONT>    <a name="line.3594"></a>
<FONT color="green">3595</FONT>                }<a name="line.3595"></a>
<FONT color="green">3596</FONT>    <a name="line.3596"></a>
<FONT color="green">3597</FONT>            }<a name="line.3597"></a>
<FONT color="green">3598</FONT>        }<a name="line.3598"></a>
<FONT color="green">3599</FONT>    <a name="line.3599"></a>
<FONT color="green">3600</FONT>        /**<a name="line.3600"></a>
<FONT color="green">3601</FONT>         * Computes the remainder as prescribed by the IEEE 754 standard.<a name="line.3601"></a>
<FONT color="green">3602</FONT>         * The remainder value is mathematically equal to {@code x - y*n}<a name="line.3602"></a>
<FONT color="green">3603</FONT>         * where {@code n} is the mathematical integer closest to the exact mathematical value<a name="line.3603"></a>
<FONT color="green">3604</FONT>         * of the quotient {@code x/y}.<a name="line.3604"></a>
<FONT color="green">3605</FONT>         * If two mathematical integers are equally close to {@code x/y} then<a name="line.3605"></a>
<FONT color="green">3606</FONT>         * {@code n} is the integer that is even.<a name="line.3606"></a>
<FONT color="green">3607</FONT>         * &lt;p&gt;<a name="line.3607"></a>
<FONT color="green">3608</FONT>         * &lt;ul&gt;<a name="line.3608"></a>
<FONT color="green">3609</FONT>         * &lt;li&gt;If either operand is NaN, the result is NaN.&lt;/li&gt;<a name="line.3609"></a>
<FONT color="green">3610</FONT>         * &lt;li&gt;If the result is not NaN, the sign of the result equals the sign of the dividend.&lt;/li&gt;<a name="line.3610"></a>
<FONT color="green">3611</FONT>         * &lt;li&gt;If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.&lt;/li&gt;<a name="line.3611"></a>
<FONT color="green">3612</FONT>         * &lt;li&gt;If the dividend is finite and the divisor is an infinity, the result equals the dividend.&lt;/li&gt;<a name="line.3612"></a>
<FONT color="green">3613</FONT>         * &lt;li&gt;If the dividend is a zero and the divisor is finite, the result equals the dividend.&lt;/li&gt;<a name="line.3613"></a>
<FONT color="green">3614</FONT>         * &lt;/ul&gt;<a name="line.3614"></a>
<FONT color="green">3615</FONT>         * &lt;p&gt;&lt;b&gt;Note:&lt;/b&gt; this implementation currently delegates to {@link StrictMath#IEEEremainder}<a name="line.3615"></a>
<FONT color="green">3616</FONT>         * @param dividend the number to be divided<a name="line.3616"></a>
<FONT color="green">3617</FONT>         * @param divisor the number by which to divide<a name="line.3617"></a>
<FONT color="green">3618</FONT>         * @return the remainder, rounded<a name="line.3618"></a>
<FONT color="green">3619</FONT>         */<a name="line.3619"></a>
<FONT color="green">3620</FONT>        public static double IEEEremainder(double dividend, double divisor) {<a name="line.3620"></a>
<FONT color="green">3621</FONT>            return StrictMath.IEEEremainder(dividend, divisor); // TODO provide our own implementation<a name="line.3621"></a>
<FONT color="green">3622</FONT>        }<a name="line.3622"></a>
<FONT color="green">3623</FONT>    <a name="line.3623"></a>
<FONT color="green">3624</FONT>        /**<a name="line.3624"></a>
<FONT color="green">3625</FONT>         * Returns the first argument with the sign of the second argument.<a name="line.3625"></a>
<FONT color="green">3626</FONT>         * A NaN {@code sign} argument is treated as positive.<a name="line.3626"></a>
<FONT color="green">3627</FONT>         *<a name="line.3627"></a>
<FONT color="green">3628</FONT>         * @param magnitude the value to return<a name="line.3628"></a>
<FONT color="green">3629</FONT>         * @param sign the sign for the returned value<a name="line.3629"></a>
<FONT color="green">3630</FONT>         * @return the magnitude with the same sign as the {@code sign} argument<a name="line.3630"></a>
<FONT color="green">3631</FONT>         */<a name="line.3631"></a>
<FONT color="green">3632</FONT>        public static double copySign(double magnitude, double sign){<a name="line.3632"></a>
<FONT color="green">3633</FONT>            long m = Double.doubleToLongBits(magnitude);<a name="line.3633"></a>
<FONT color="green">3634</FONT>            long s = Double.doubleToLongBits(sign);<a name="line.3634"></a>
<FONT color="green">3635</FONT>            if ((m &gt;= 0 &amp;&amp; s &gt;= 0) || (m &lt; 0 &amp;&amp; s &lt; 0)) { // Sign is currently OK<a name="line.3635"></a>
<FONT color="green">3636</FONT>                return magnitude;<a name="line.3636"></a>
<FONT color="green">3637</FONT>            }<a name="line.3637"></a>
<FONT color="green">3638</FONT>            return -magnitude; // flip sign<a name="line.3638"></a>
<FONT color="green">3639</FONT>        }<a name="line.3639"></a>
<FONT color="green">3640</FONT>    <a name="line.3640"></a>
<FONT color="green">3641</FONT>        /**<a name="line.3641"></a>
<FONT color="green">3642</FONT>         * Returns the first argument with the sign of the second argument.<a name="line.3642"></a>
<FONT color="green">3643</FONT>         * A NaN {@code sign} argument is treated as positive.<a name="line.3643"></a>
<FONT color="green">3644</FONT>         *<a name="line.3644"></a>
<FONT color="green">3645</FONT>         * @param magnitude the value to return<a name="line.3645"></a>
<FONT color="green">3646</FONT>         * @param sign the sign for the returned value<a name="line.3646"></a>
<FONT color="green">3647</FONT>         * @return the magnitude with the same sign as the {@code sign} argument<a name="line.3647"></a>
<FONT color="green">3648</FONT>         */<a name="line.3648"></a>
<FONT color="green">3649</FONT>        public static float copySign(float magnitude, float sign){<a name="line.3649"></a>
<FONT color="green">3650</FONT>            int m = Float.floatToIntBits(magnitude);<a name="line.3650"></a>
<FONT color="green">3651</FONT>            int s = Float.floatToIntBits(sign);<a name="line.3651"></a>
<FONT color="green">3652</FONT>            if ((m &gt;= 0 &amp;&amp; s &gt;= 0) || (m &lt; 0 &amp;&amp; s &lt; 0)) { // Sign is currently OK<a name="line.3652"></a>
<FONT color="green">3653</FONT>                return magnitude;<a name="line.3653"></a>
<FONT color="green">3654</FONT>            }<a name="line.3654"></a>
<FONT color="green">3655</FONT>            return -magnitude; // flip sign<a name="line.3655"></a>
<FONT color="green">3656</FONT>        }<a name="line.3656"></a>
<FONT color="green">3657</FONT>    <a name="line.3657"></a>
<FONT color="green">3658</FONT>        /**<a name="line.3658"></a>
<FONT color="green">3659</FONT>         * Return the exponent of a double number, removing the bias.<a name="line.3659"></a>
<FONT color="green">3660</FONT>         * &lt;p&gt;<a name="line.3660"></a>
<FONT color="green">3661</FONT>         * For double numbers of the form 2&lt;sup&gt;x&lt;/sup&gt;, the unbiased<a name="line.3661"></a>
<FONT color="green">3662</FONT>         * exponent is exactly x.<a name="line.3662"></a>
<FONT color="green">3663</FONT>         * &lt;/p&gt;<a name="line.3663"></a>
<FONT color="green">3664</FONT>         * @param d number from which exponent is requested<a name="line.3664"></a>
<FONT color="green">3665</FONT>         * @return exponent for d in IEEE754 representation, without bias<a name="line.3665"></a>
<FONT color="green">3666</FONT>         */<a name="line.3666"></a>
<FONT color="green">3667</FONT>        public static int getExponent(final double d) {<a name="line.3667"></a>
<FONT color="green">3668</FONT>            return (int) ((Double.doubleToLongBits(d) &gt;&gt;&gt; 52) &amp; 0x7ff) - 1023;<a name="line.3668"></a>
<FONT color="green">3669</FONT>        }<a name="line.3669"></a>
<FONT color="green">3670</FONT>    <a name="line.3670"></a>
<FONT color="green">3671</FONT>        /**<a name="line.3671"></a>
<FONT color="green">3672</FONT>         * Return the exponent of a float number, removing the bias.<a name="line.3672"></a>
<FONT color="green">3673</FONT>         * &lt;p&gt;<a name="line.3673"></a>
<FONT color="green">3674</FONT>         * For float numbers of the form 2&lt;sup&gt;x&lt;/sup&gt;, the unbiased<a name="line.3674"></a>
<FONT color="green">3675</FONT>         * exponent is exactly x.<a name="line.3675"></a>
<FONT color="green">3676</FONT>         * &lt;/p&gt;<a name="line.3676"></a>
<FONT color="green">3677</FONT>         * @param f number from which exponent is requested<a name="line.3677"></a>
<FONT color="green">3678</FONT>         * @return exponent for d in IEEE754 representation, without bias<a name="line.3678"></a>
<FONT color="green">3679</FONT>         */<a name="line.3679"></a>
<FONT color="green">3680</FONT>        public static int getExponent(final float f) {<a name="line.3680"></a>
<FONT color="green">3681</FONT>            return ((Float.floatToIntBits(f) &gt;&gt;&gt; 23) &amp; 0xff) - 127;<a name="line.3681"></a>
<FONT color="green">3682</FONT>        }<a name="line.3682"></a>
<FONT color="green">3683</FONT>    <a name="line.3683"></a>
<FONT color="green">3684</FONT>        /**<a name="line.3684"></a>
<FONT color="green">3685</FONT>         * Print out contents of arrays, and check the length.<a name="line.3685"></a>
<FONT color="green">3686</FONT>         * &lt;p&gt;used to generate the preset arrays originally.&lt;/p&gt;<a name="line.3686"></a>
<FONT color="green">3687</FONT>         * @param a unused<a name="line.3687"></a>
<FONT color="green">3688</FONT>         */<a name="line.3688"></a>
<FONT color="green">3689</FONT>        public static void main(String[] a) {<a name="line.3689"></a>
<FONT color="green">3690</FONT>            PrintStream out = System.out;<a name="line.3690"></a>
<FONT color="green">3691</FONT>            FastMathCalc.printarray(out, "EXP_INT_TABLE_A", EXP_INT_TABLE_LEN, ExpIntTable.EXP_INT_TABLE_A);<a name="line.3691"></a>
<FONT color="green">3692</FONT>            FastMathCalc.printarray(out, "EXP_INT_TABLE_B", EXP_INT_TABLE_LEN, ExpIntTable.EXP_INT_TABLE_B);<a name="line.3692"></a>
<FONT color="green">3693</FONT>            FastMathCalc.printarray(out, "EXP_FRAC_TABLE_A", EXP_FRAC_TABLE_LEN, ExpFracTable.EXP_FRAC_TABLE_A);<a name="line.3693"></a>
<FONT color="green">3694</FONT>            FastMathCalc.printarray(out, "EXP_FRAC_TABLE_B", EXP_FRAC_TABLE_LEN, ExpFracTable.EXP_FRAC_TABLE_B);<a name="line.3694"></a>
<FONT color="green">3695</FONT>            FastMathCalc.printarray(out, "LN_MANT",LN_MANT_LEN, lnMant.LN_MANT);<a name="line.3695"></a>
<FONT color="green">3696</FONT>            FastMathCalc.printarray(out, "SINE_TABLE_A", SINE_TABLE_LEN, SINE_TABLE_A);<a name="line.3696"></a>
<FONT color="green">3697</FONT>            FastMathCalc.printarray(out, "SINE_TABLE_B", SINE_TABLE_LEN, SINE_TABLE_B);<a name="line.3697"></a>
<FONT color="green">3698</FONT>            FastMathCalc.printarray(out, "COSINE_TABLE_A", SINE_TABLE_LEN, COSINE_TABLE_A);<a name="line.3698"></a>
<FONT color="green">3699</FONT>            FastMathCalc.printarray(out, "COSINE_TABLE_B", SINE_TABLE_LEN, COSINE_TABLE_B);<a name="line.3699"></a>
<FONT color="green">3700</FONT>            FastMathCalc.printarray(out, "TANGENT_TABLE_A", SINE_TABLE_LEN, TANGENT_TABLE_A);<a name="line.3700"></a>
<FONT color="green">3701</FONT>            FastMathCalc.printarray(out, "TANGENT_TABLE_B", SINE_TABLE_LEN, TANGENT_TABLE_B);<a name="line.3701"></a>
<FONT color="green">3702</FONT>        }<a name="line.3702"></a>
<FONT color="green">3703</FONT>    <a name="line.3703"></a>
<FONT color="green">3704</FONT>        /** Enclose large data table in nested static class so it's only loaded on first access. */<a name="line.3704"></a>
<FONT color="green">3705</FONT>        private static class ExpIntTable {<a name="line.3705"></a>
<FONT color="green">3706</FONT>            /** Exponential evaluated at integer values,<a name="line.3706"></a>
<FONT color="green">3707</FONT>             * exp(x) =  expIntTableA[x + EXP_INT_TABLE_MAX_INDEX] + expIntTableB[x+EXP_INT_TABLE_MAX_INDEX].<a name="line.3707"></a>
<FONT color="green">3708</FONT>             */<a name="line.3708"></a>
<FONT color="green">3709</FONT>            private static final double[] EXP_INT_TABLE_A;<a name="line.3709"></a>
<FONT color="green">3710</FONT>            /** Exponential evaluated at integer values,<a name="line.3710"></a>
<FONT color="green">3711</FONT>             * exp(x) =  expIntTableA[x + EXP_INT_TABLE_MAX_INDEX] + expIntTableB[x+EXP_INT_TABLE_MAX_INDEX]<a name="line.3711"></a>
<FONT color="green">3712</FONT>             */<a name="line.3712"></a>
<FONT color="green">3713</FONT>            private static final double[] EXP_INT_TABLE_B;<a name="line.3713"></a>
<FONT color="green">3714</FONT>    <a name="line.3714"></a>
<FONT color="green">3715</FONT>            static {<a name="line.3715"></a>
<FONT color="green">3716</FONT>                if (RECOMPUTE_TABLES_AT_RUNTIME) {<a name="line.3716"></a>
<FONT color="green">3717</FONT>                    EXP_INT_TABLE_A = new double[FastMath.EXP_INT_TABLE_LEN];<a name="line.3717"></a>
<FONT color="green">3718</FONT>                    EXP_INT_TABLE_B = new double[FastMath.EXP_INT_TABLE_LEN];<a name="line.3718"></a>
<FONT color="green">3719</FONT>    <a name="line.3719"></a>
<FONT color="green">3720</FONT>                    final double tmp[] = new double[2];<a name="line.3720"></a>
<FONT color="green">3721</FONT>                    final double recip[] = new double[2];<a name="line.3721"></a>
<FONT color="green">3722</FONT>    <a name="line.3722"></a>
<FONT color="green">3723</FONT>                    // Populate expIntTable<a name="line.3723"></a>
<FONT color="green">3724</FONT>                    for (int i = 0; i &lt; FastMath.EXP_INT_TABLE_MAX_INDEX; i++) {<a name="line.3724"></a>
<FONT color="green">3725</FONT>                        FastMathCalc.expint(i, tmp);<a name="line.3725"></a>
<FONT color="green">3726</FONT>                        EXP_INT_TABLE_A[i + FastMath.EXP_INT_TABLE_MAX_INDEX] = tmp[0];<a name="line.3726"></a>
<FONT color="green">3727</FONT>                        EXP_INT_TABLE_B[i + FastMath.EXP_INT_TABLE_MAX_INDEX] = tmp[1];<a name="line.3727"></a>
<FONT color="green">3728</FONT>    <a name="line.3728"></a>
<FONT color="green">3729</FONT>                        if (i != 0) {<a name="line.3729"></a>
<FONT color="green">3730</FONT>                            // Negative integer powers<a name="line.3730"></a>
<FONT color="green">3731</FONT>                            FastMathCalc.splitReciprocal(tmp, recip);<a name="line.3731"></a>
<FONT color="green">3732</FONT>                            EXP_INT_TABLE_A[FastMath.EXP_INT_TABLE_MAX_INDEX - i] = recip[0];<a name="line.3732"></a>
<FONT color="green">3733</FONT>                            EXP_INT_TABLE_B[FastMath.EXP_INT_TABLE_MAX_INDEX - i] = recip[1];<a name="line.3733"></a>
<FONT color="green">3734</FONT>                        }<a name="line.3734"></a>
<FONT color="green">3735</FONT>                    }<a name="line.3735"></a>
<FONT color="green">3736</FONT>                } else {<a name="line.3736"></a>
<FONT color="green">3737</FONT>                    EXP_INT_TABLE_A = FastMathLiteralArrays.loadExpIntA();<a name="line.3737"></a>
<FONT color="green">3738</FONT>                    EXP_INT_TABLE_B = FastMathLiteralArrays.loadExpIntB();<a name="line.3738"></a>
<FONT color="green">3739</FONT>                }<a name="line.3739"></a>
<FONT color="green">3740</FONT>            }<a name="line.3740"></a>
<FONT color="green">3741</FONT>        }<a name="line.3741"></a>
<FONT color="green">3742</FONT>    <a name="line.3742"></a>
<FONT color="green">3743</FONT>        /** Enclose large data table in nested static class so it's only loaded on first access. */<a name="line.3743"></a>
<FONT color="green">3744</FONT>        private static class ExpFracTable {<a name="line.3744"></a>
<FONT color="green">3745</FONT>            /** Exponential over the range of 0 - 1 in increments of 2^-10<a name="line.3745"></a>
<FONT color="green">3746</FONT>             * exp(x/1024) =  expFracTableA[x] + expFracTableB[x].<a name="line.3746"></a>
<FONT color="green">3747</FONT>             * 1024 = 2^10<a name="line.3747"></a>
<FONT color="green">3748</FONT>             */<a name="line.3748"></a>
<FONT color="green">3749</FONT>            private static final double[] EXP_FRAC_TABLE_A;<a name="line.3749"></a>
<FONT color="green">3750</FONT>            /** Exponential over the range of 0 - 1 in increments of 2^-10<a name="line.3750"></a>
<FONT color="green">3751</FONT>             * exp(x/1024) =  expFracTableA[x] + expFracTableB[x].<a name="line.3751"></a>
<FONT color="green">3752</FONT>             */<a name="line.3752"></a>
<FONT color="green">3753</FONT>            private static final double[] EXP_FRAC_TABLE_B;<a name="line.3753"></a>
<FONT color="green">3754</FONT>    <a name="line.3754"></a>
<FONT color="green">3755</FONT>            static {<a name="line.3755"></a>
<FONT color="green">3756</FONT>                if (RECOMPUTE_TABLES_AT_RUNTIME) {<a name="line.3756"></a>
<FONT color="green">3757</FONT>                    EXP_FRAC_TABLE_A = new double[FastMath.EXP_FRAC_TABLE_LEN];<a name="line.3757"></a>
<FONT color="green">3758</FONT>                    EXP_FRAC_TABLE_B = new double[FastMath.EXP_FRAC_TABLE_LEN];<a name="line.3758"></a>
<FONT color="green">3759</FONT>    <a name="line.3759"></a>
<FONT color="green">3760</FONT>                    final double tmp[] = new double[2];<a name="line.3760"></a>
<FONT color="green">3761</FONT>    <a name="line.3761"></a>
<FONT color="green">3762</FONT>                    // Populate expFracTable<a name="line.3762"></a>
<FONT color="green">3763</FONT>                    final double factor = 1d / (EXP_FRAC_TABLE_LEN - 1);<a name="line.3763"></a>
<FONT color="green">3764</FONT>                    for (int i = 0; i &lt; EXP_FRAC_TABLE_A.length; i++) {<a name="line.3764"></a>
<FONT color="green">3765</FONT>                        FastMathCalc.slowexp(i * factor, tmp);<a name="line.3765"></a>
<FONT color="green">3766</FONT>                        EXP_FRAC_TABLE_A[i] = tmp[0];<a name="line.3766"></a>
<FONT color="green">3767</FONT>                        EXP_FRAC_TABLE_B[i] = tmp[1];<a name="line.3767"></a>
<FONT color="green">3768</FONT>                    }<a name="line.3768"></a>
<FONT color="green">3769</FONT>                } else {<a name="line.3769"></a>
<FONT color="green">3770</FONT>                    EXP_FRAC_TABLE_A = FastMathLiteralArrays.loadExpFracA();<a name="line.3770"></a>
<FONT color="green">3771</FONT>                    EXP_FRAC_TABLE_B = FastMathLiteralArrays.loadExpFracB();<a name="line.3771"></a>
<FONT color="green">3772</FONT>                }<a name="line.3772"></a>
<FONT color="green">3773</FONT>            }<a name="line.3773"></a>
<FONT color="green">3774</FONT>        }<a name="line.3774"></a>
<FONT color="green">3775</FONT>    <a name="line.3775"></a>
<FONT color="green">3776</FONT>        /** Enclose large data table in nested static class so it's only loaded on first access. */<a name="line.3776"></a>
<FONT color="green">3777</FONT>        private static class lnMant {<a name="line.3777"></a>
<FONT color="green">3778</FONT>            /** Extended precision logarithm table over the range 1 - 2 in increments of 2^-10. */<a name="line.3778"></a>
<FONT color="green">3779</FONT>            private static final double[][] LN_MANT;<a name="line.3779"></a>
<FONT color="green">3780</FONT>    <a name="line.3780"></a>
<FONT color="green">3781</FONT>            static {<a name="line.3781"></a>
<FONT color="green">3782</FONT>                if (RECOMPUTE_TABLES_AT_RUNTIME) {<a name="line.3782"></a>
<FONT color="green">3783</FONT>                    LN_MANT = new double[FastMath.LN_MANT_LEN][];<a name="line.3783"></a>
<FONT color="green">3784</FONT>    <a name="line.3784"></a>
<FONT color="green">3785</FONT>                    // Populate lnMant table<a name="line.3785"></a>
<FONT color="green">3786</FONT>                    for (int i = 0; i &lt; LN_MANT.length; i++) {<a name="line.3786"></a>
<FONT color="green">3787</FONT>                        final double d = Double.longBitsToDouble( (((long) i) &lt;&lt; 42) | 0x3ff0000000000000L );<a name="line.3787"></a>
<FONT color="green">3788</FONT>                        LN_MANT[i] = FastMathCalc.slowLog(d);<a name="line.3788"></a>
<FONT color="green">3789</FONT>                    }<a name="line.3789"></a>
<FONT color="green">3790</FONT>                } else {<a name="line.3790"></a>
<FONT color="green">3791</FONT>                    LN_MANT = FastMathLiteralArrays.loadLnMant();<a name="line.3791"></a>
<FONT color="green">3792</FONT>                }<a name="line.3792"></a>
<FONT color="green">3793</FONT>            }<a name="line.3793"></a>
<FONT color="green">3794</FONT>        }<a name="line.3794"></a>
<FONT color="green">3795</FONT>    <a name="line.3795"></a>
<FONT color="green">3796</FONT>        /** Enclose the Cody/Waite reduction (used in "sin", "cos" and "tan"). */<a name="line.3796"></a>
<FONT color="green">3797</FONT>        private static class CodyWaite {<a name="line.3797"></a>
<FONT color="green">3798</FONT>            /** k */<a name="line.3798"></a>
<FONT color="green">3799</FONT>            private final int finalK;<a name="line.3799"></a>
<FONT color="green">3800</FONT>            /** remA */<a name="line.3800"></a>
<FONT color="green">3801</FONT>            private final double finalRemA;<a name="line.3801"></a>
<FONT color="green">3802</FONT>            /** remB */<a name="line.3802"></a>
<FONT color="green">3803</FONT>            private final double finalRemB;<a name="line.3803"></a>
<FONT color="green">3804</FONT>    <a name="line.3804"></a>
<FONT color="green">3805</FONT>            /**<a name="line.3805"></a>
<FONT color="green">3806</FONT>             * @param xa Argument.<a name="line.3806"></a>
<FONT color="green">3807</FONT>             */<a name="line.3807"></a>
<FONT color="green">3808</FONT>            CodyWaite(double xa) {<a name="line.3808"></a>
<FONT color="green">3809</FONT>                // Estimate k.<a name="line.3809"></a>
<FONT color="green">3810</FONT>                //k = (int)(xa / 1.5707963267948966);<a name="line.3810"></a>
<FONT color="green">3811</FONT>                int k = (int)(xa * 0.6366197723675814);<a name="line.3811"></a>
<FONT color="green">3812</FONT>    <a name="line.3812"></a>
<FONT color="green">3813</FONT>                // Compute remainder.<a name="line.3813"></a>
<FONT color="green">3814</FONT>                double remA;<a name="line.3814"></a>
<FONT color="green">3815</FONT>                double remB;<a name="line.3815"></a>
<FONT color="green">3816</FONT>                while (true) {<a name="line.3816"></a>
<FONT color="green">3817</FONT>                    double a = -k * 1.570796251296997;<a name="line.3817"></a>
<FONT color="green">3818</FONT>                    remA = xa + a;<a name="line.3818"></a>
<FONT color="green">3819</FONT>                    remB = -(remA - xa - a);<a name="line.3819"></a>
<FONT color="green">3820</FONT>    <a name="line.3820"></a>
<FONT color="green">3821</FONT>                    a = -k * 7.549789948768648E-8;<a name="line.3821"></a>
<FONT color="green">3822</FONT>                    double b = remA;<a name="line.3822"></a>
<FONT color="green">3823</FONT>                    remA = a + b;<a name="line.3823"></a>
<FONT color="green">3824</FONT>                    remB += -(remA - b - a);<a name="line.3824"></a>
<FONT color="green">3825</FONT>    <a name="line.3825"></a>
<FONT color="green">3826</FONT>                    a = -k * 6.123233995736766E-17;<a name="line.3826"></a>
<FONT color="green">3827</FONT>                    b = remA;<a name="line.3827"></a>
<FONT color="green">3828</FONT>                    remA = a + b;<a name="line.3828"></a>
<FONT color="green">3829</FONT>                    remB += -(remA - b - a);<a name="line.3829"></a>
<FONT color="green">3830</FONT>    <a name="line.3830"></a>
<FONT color="green">3831</FONT>                    if (remA &gt; 0) {<a name="line.3831"></a>
<FONT color="green">3832</FONT>                        break;<a name="line.3832"></a>
<FONT color="green">3833</FONT>                    }<a name="line.3833"></a>
<FONT color="green">3834</FONT>    <a name="line.3834"></a>
<FONT color="green">3835</FONT>                    // Remainder is negative, so decrement k and try again.<a name="line.3835"></a>
<FONT color="green">3836</FONT>                    // This should only happen if the input is very close<a name="line.3836"></a>
<FONT color="green">3837</FONT>                    // to an even multiple of pi/2.<a name="line.3837"></a>
<FONT color="green">3838</FONT>                    --k;<a name="line.3838"></a>
<FONT color="green">3839</FONT>                }<a name="line.3839"></a>
<FONT color="green">3840</FONT>    <a name="line.3840"></a>
<FONT color="green">3841</FONT>                this.finalK = k;<a name="line.3841"></a>
<FONT color="green">3842</FONT>                this.finalRemA = remA;<a name="line.3842"></a>
<FONT color="green">3843</FONT>                this.finalRemB = remB;<a name="line.3843"></a>
<FONT color="green">3844</FONT>            }<a name="line.3844"></a>
<FONT color="green">3845</FONT>    <a name="line.3845"></a>
<FONT color="green">3846</FONT>            /**<a name="line.3846"></a>
<FONT color="green">3847</FONT>             * @return k<a name="line.3847"></a>
<FONT color="green">3848</FONT>             */<a name="line.3848"></a>
<FONT color="green">3849</FONT>            int getK() {<a name="line.3849"></a>
<FONT color="green">3850</FONT>                return finalK;<a name="line.3850"></a>
<FONT color="green">3851</FONT>            }<a name="line.3851"></a>
<FONT color="green">3852</FONT>            /**<a name="line.3852"></a>
<FONT color="green">3853</FONT>             * @return remA<a name="line.3853"></a>
<FONT color="green">3854</FONT>             */<a name="line.3854"></a>
<FONT color="green">3855</FONT>            double getRemA() {<a name="line.3855"></a>
<FONT color="green">3856</FONT>                return finalRemA;<a name="line.3856"></a>
<FONT color="green">3857</FONT>            }<a name="line.3857"></a>
<FONT color="green">3858</FONT>            /**<a name="line.3858"></a>
<FONT color="green">3859</FONT>             * @return remB<a name="line.3859"></a>
<FONT color="green">3860</FONT>             */<a name="line.3860"></a>
<FONT color="green">3861</FONT>            double getRemB() {<a name="line.3861"></a>
<FONT color="green">3862</FONT>                return finalRemB;<a name="line.3862"></a>
<FONT color="green">3863</FONT>            }<a name="line.3863"></a>
<FONT color="green">3864</FONT>        }<a name="line.3864"></a>
<FONT color="green">3865</FONT>    }<a name="line.3865"></a>




























































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